One-Dimensional Simulation of PM Deposition and Regeneration in Particulate Filters: Optimal Conditions for PM Oxidation in GPF Considering Oxygen Concentration and Temperature

Abstract

This study presents a one-dimensional numerical simulation of particulate matter (PM) oxidation and regeneration behavior in gasoline particulate filters (GPFs) under Worldwide Harmonized Light Vehicles Test Cycle (WLTC) conditions. The model incorporates both catalyst activity—represented by activation energy (E) and pre-exponential factor (A)—and exhaust control strategies involving forced fuel cut (FC). PM deposition and oxidation were simulated based on solid-state and gas-phase reactions, with the effects of oxygen concentration and temperature analyzed in detail. The results show that under high catalyst activity (E = 100 kJ mol⁻¹, A = 6.2 × 10⁷), PM oxidation proceeds efficiently even during medium-speed phases, achieving a 98.8% oxidation rate after one WLTC. Conversely, conventional catalysts (E = 120 kJ mol⁻¹, A = 6.2 × 10⁶) exhibited limited regeneration, leaving 0.11 g of residual PM. Introducing forced FC effectively enhanced oxidation by increasing oxygen concentration to 20% and sustaining heat release. A single continuous 100 s FC yielded the highest oxidation (96% reduction), while split FCs reduced peak PM accumulation. These findings demonstrate that optimizing the balance between catalyst activity and FC control can significantly improve GPF regeneration performance, providing a practical strategy for PM reduction in GDI vehicles under real driving conditions.

1. Introduction

In recent years, gasoline vehicles—both port fuel injection (PFI) and gasoline direct injection (GDI)—have advanced in a way that simultaneously improves fuel economy and power output. In particular, GDI increases freedom in combustion control by injecting fuel directly into the chamber, enabling higher compression ratios and lean operation that raise thermal efficiency and torque. At the same time, growing concern over ultrafine particle exposure has prompted regulatory tightening: Euro 7 requires all spark-ignition (i.e., gasoline) cars and vans to meet particulate matter (PM) mass and particle-number limits down to 10 nm (PN10). This scope now includes PFI, which had been exempt from PN limits under Euro 6. However, the direct-injection configuration is especially prone to wall impingement and ignition-delay-related incomplete combustion, increasing the propensity for carbonaceous residues and hence particulate matter (PM) formation. As a result, GDI applications have seen accelerated deployment and study of gasoline particulate filters (GPF) and related control strategies; with Euro 7, particle control is mandated across all gasoline technologies, not only GDI. Recent reviews emphasize that this tightening of PN limits (down to 10 nm) under Euro 7 now covers even port fuel injection (PFI) vehicles, and has driven substantial research into filter design and control integration. Moreover, Euro 7’s broader durability and temperature-window requirements are expected to further reshape exhaust after-treatment architectures [1,2,3,4].

Accordingly, while Euro 7 mandates particle control across all gasoline technologies, we focus next on the GDI-dominant pathways of PM formation and on GPF-based regeneration under WLTC-representative oxygen and temperature windows. The amount of PM emitted from GDI vehicles is reported to be significantly higher than that from conventional port fuel injection gasoline vehicles—up to 28 times higher under the JC08 cold mode and 170 times higher under the JC08 hot mode [5]. Furthermore, PM generated from GDI engines is primarily in the size range of 10–70 nm, which is smaller than PM from diesel engines. These nanosized particles can penetrate the human body via the respiratory tract, potentially affecting the alveoli and cardiovascular system [6,7]. Thus, PM emissions from GDI engines have attracted attention as a new environmental and health risk. Against this background, regulations on particulate matter (PM) emissions from gasoline vehicles have been increasingly tightened, particularly in Europe. In response, the installation of Gasoline Particle Filters (GPF) is being promoted as a countermeasure. GPFs are wall-flow filters with a structure similar to Diesel Particle Filters (DPF). They filter exhaust gases through porous ceramics, capturing, storing, and oxidizing PM [8,9,10,11,12,13,14,15]. GPFs are wall-flow filters with a structure similar to Diesel Particulate Filters (DPF). They filter exhaust gases through porous ceramics, capturing, storing, and oxidizing PM. Extensive studies have been conducted to elucidate soot deposition and regeneration behaviors on such filter structures [16,17,18,19,20].

A GPF consists of ceramic channels that are alternately sealed at one end. Exhaust gases enter through the inlet channels and pass through the porous walls, where PM is trapped on the wall surface, and only the cleaned gas is discharged through the outlet channels (Figure 1a). As PM accumulates, it clogs the pores and wall surfaces, increasing the pressure drop (ΔP) between the inlet and outlet, which may negatively affect engine performance and fuel economy (Figure 1b). Therefore, a “regeneration process” is required regularly to burn off and remove the accumulated PM.

The primary component of PM is carbon, which, in principle, can be oxidized under atmospheric conditions with 20% oxygen at temperatures above 650 °C. However, the oxygen concentration and temperature of GDI exhaust gases vary greatly depending on the engine combustion state and the configuration of the three-way catalyst (TWC), and conditions suitable for GPF regeneration are not always achieved. To overcome these limitations, numerous studies have investigated soot oxidation over various catalysts—such as noble metals, perovskite-type oxides, and ceria-based materials—to lower the activation temperature and enhance regeneration efficiency [21,22,23,24,25,26,27,28]

When the GPF is installed downstream of the TWC, the exhaust gas encounters a reducing atmosphere and remains at relatively low temperatures (250–500 °C). In contrast, when the TWC and GPF are integrated into a single unit, the exhaust temperature can increase to around 700 °C [29]. These differences indicate that exhaust system configuration strongly influences the achievable regeneration temperature.

Figure 1. Illustration of the soot trapping system. (a) Shows a cross-section of the GPF. Exhaust gas containing PM enters the GPF, where the filter removes only the PM, discharging only clean gas. (b) Shows the interior wall of the GPF. Exhaust gas flows from above, and PM is captured by the middle wall (porous) [30,31,32,33].

Figure 1. Illustration of the soot trapping system. (a) Shows a cross-section of the GPF. Exhaust gas containing PM enters the GPF, where the filter removes only the PM, discharging only clean gas. (b) Shows the interior wall of the GPF. Exhaust gas flows from above, and PM is captured by the middle wall (porous) [30,31,32,33].

In addition to temperature, oxygen availability also varies markedly during real-world driving. As shown in Figure 2, during the WLTC mode the oxygen concentration spikes to approximately 20% during brief deceleration periods; however, these high-oxygen episodes last only a few to several seconds. For the majority of the cycle, the oxygen level remains below 1%, representing a persistently low-oxygen environment. Consequently, periods during which both high temperature and sufficient oxygen coexist—conditions required for effective PM oxidation—are extremely limited.

The FC operation must be planned by the total design of exhaust treatment of both TWC and PM oxidation. The present FC operation is planned at temperatures ranging from 700 to 800 °C and the TWC catalysis is expected to exhibit satisfactory performance without serious degradation. The feasibility of such heat stable catalytic converters is contingent upon the utilization of the most advanced GPF (and TWC) converter. Consequently, it can be concluded that the additional FC strategy discussed in this study can be applied to the present TWC system, provided that state-of-the-art, thermally durable GPF and TWC converters are employed.

To address these challenges, our earlier work [30,31,32,33] analyzed PM oxidation using a rate-equation model. Building on this framework, the present study incorporates kinetic parameters—activation energy (E) and pre-exponential factor (A)—based on previously reported values and evaluates their influence on oxidation behavior under realistic exhaust conditions. Consistent with prior findings, conventional catalyst properties (e.g., E ≈ 120 kJ mol⁻¹ and A ≈ 6.2 × 10⁶) do not promote sufficient PM oxidation under typical GPF operating conditions, resulting in considerable residual PM. In contrast, when E is reduced to approximately 100 kJ mol⁻¹, the rate-equation model predicts that oxidation proceeds more readily during high-temperature phases of the driving cycle. In addition to these kinetic parameters, the effect of oxygen concentration was examined to clarify the conditions under which PM oxidation can occur. As shown in Figure 3, the PM fraction decreases only gradually at low oxygen availability (e.g., 1% O₂). However, at higher oxygen concentrations, such as 20%, rapid oxidation occurs within several seconds, leading to significant PM removal. These results highlight that even short periods of elevated oxygen concentration can strongly accelerate PM oxidation, and that both kinetic parameters and transient oxygen spikes play a critical role in governing regeneration behavior.

2. Calculation Model

In this study, numerical simulations were performed using a GPF-specific one-dimensional model that has been developed and validated in our previous work [30,31,32,33]. Only the main assumptions and governing equations are summarized below; further details can be found in the cited references. The GPF is treated as a cylindrical monolith with diameter D and length L. The axial direction (defined as the x-direction) is discretized into n equally spaced control volumes (cells). In each axial cell, the flow domain is divided into three regions: the inlet channel, the porous filter wall, and the outlet channel. Within the wall, the thickness direction is defined as the y-direction and is similarly discretized into n equally spaced segments. This layered representation allows us to resolve transport and reaction both along the flow direction and across the wall thickness.

2.1. Exhaust Gas Flow in the Axial Direction (x-Direction) of the GPF

The total exhaust gas volumetric flow rate entering the GPF is denoted by ΣFi [m³/s]. This total flow is distributed among the n axial cells according to

$${\mathsf{\Sigma }}_{i=1}^n{F}_i=∆F_1+∆F_2+\dots +∆F_n$$

(1)

The flow rate in the i-th, F_i, is expressed as

$$F_{ni}=v_{ni}\times \sigma$$

(2)

where F_i [m³/s] is the volumetric flow rate in cell i, v_i [m/s] is the superficial gas velocity, and σ [m²] is the cross-sectional area of the flow path. The corresponding pressure drop is given by

$$∆P=\lambda {\displaystyle \frac{L_{WP+PM}}{D_{walls}}}·{\displaystyle \frac{v_i^2}{2}}·\rho$$

(3)

where λ is the pipe friction coefficient, L_WP+PM is the flow length [m], D_walls is the wall diameter [m], v is the average velocity [m/s], and ρ is the fluid density [kg/m³]. At the initial stage of PM deposition (i.e., when loading starts from a clean filter), the exhaust gas containing PM is assumed to be distributed uniformly among all axial cells. When the gas flows in the y-direction (into the wall), the pressure in the wall-normal direction is taken to be uniform across all cells. The numerical solution is obtained cell by cell along the x-direction: the state in cell i is computed and then used as the inlet condition for cell i + 1. In the present model, the x-direction corresponds to the axial direction of the GPF along the exhaust gas flow. The y-direction represents the wall-normal direction, i.e., the direction of gas permeation into the porous wall. The symbol n denotes the total number of discretized axial cells in the x-direction, and i (i = 1, 2, …, n) represents the axial cell index. On this basis, PM deposition within the wall, temperature evolution, PM oxidation, and the spatial location of the oxidation reactions are evaluated as described below.

2.2. PM Deposition Within the GPF Wall

PM deposition behavior inside the wall is modeled based on previous experimental observations. Shortly after the onset of loading, soot tends to form a bridging layer at a position on the order of several tens of micrometers from the wall surface; subsequent deposition then proceeds mainly near this region rather than uniformly over the entire wall thickness. In addition, the wall porosity has been reported to vary in the direction from the surface toward the interior [31,34].

To capture these effects in a tractable way, the present study assumes that the local PM deposition rate decreases exponentially with depth from the wall surface toward the interior. In other words, most of the deposited PM is concentrated near the wall surface, and the contribution from deeper layers becomes progressively smaller with increasing y-position. This depth-dependent deposition profile is implemented on the y-direction grid described above.

2.3. Treatment of Temperature

For the thermal description, the following assumptions are imposed. First, heat transfer between individual PM particles is neglected, and during PM oxidation the gas temperature is assumed to be identical to the PM temperature. Radiative and convective heat exchange associated with PM particles is also neglected, because soot particles are typically only a few micrometers in size and sparsely dispersed in the gas phase. Under these assumptions, the heat capacity Q [J/K] of a single computational cell is written as

$$Q=C_{c}Vdc\left(1-\mu \right)+S{C}_g$$

(4)

where V₍d₎ [mL] is the deposited solid volume, S [mol] is the amount of gas flowing through the cell, μ is the permeability of the GPF wall, C₍c₎ [J/(g·K)] is the specific heat of the wall material (cordierite), d₍c₎ [kg/m³] is the density of the wall material, and C₍g₎ [J/(g·K)] is the specific heat of the exhaust gas. The cumulative amount of PM reacted in a cell, R₍pm₎ [mol], is defined as

$$R_{pm}=PM\left(t\right)={\int }_0^t{\displaystyle \frac{dPM}{{dt}^{\prime }}}d{t}^{\prime },$$

(5)

where PM is the amount of carbonaceous particulate matter present in the cell. The temperature rise caused by PM oxidation, ΔT [°C], is then given by

$$∆T={\displaystyle \frac{R_{pm}}{Q}}$$

(6)

After reaction, the PM particles are assumed to maintain this temperature. The gas temperature is also assumed to be uniform within the cell and is convected downstream from cell i to cell i + 1. At the entrance of the next cell, the wall temperature on the gas-inlet side is taken to be equal to the gas temperature. When the gas temperature is sufficiently high, a correction is applied according to

$$T_R=T_w+{\displaystyle \frac{\left(T_{PM}\right)}{Q}}$$

(7)

where T_R [°C] is the corrected temperature, T_w [°C] is the wall temperature, and T_PM [°C] is the combustion temperature of PM. Along the y-direction (between wall-normal segments j and j + 1), the local temperature is updated by considering heat generation due to PM oxidation if PM is present, and by heat loss to the surroundings if PM is absent. Along the x-direction (between axial cells i and i + 1), heat accumulation due to PM oxidation causes a progressive rise in gas and wall temperature, which is captured through the coupled solution of the above energy balance.

2.4. PM Oxidation

The PM oxidation is treated as a first-order complete combustion of carbon:

$$soot\left(C\right)+O_2\to {CO}_2$$

(8)

The rate of PM oxidation per unit time is given by:

$${\displaystyle \frac{dPM}{dt}}=Aexp\left(-{\displaystyle \frac{E}{RT}}\right)V{O}_2·PM$$

(9)

where A [m³/(mol·s)] is the pre-exponential factor, PM [mol] is the amount of PM, E [kJ/mol] is the activation energy, R [J/(K·mol)] is the gas constant, and T [K] is the absolute temperature, and V₍O₂₎ is a factor representing the local oxygen availability.

2.5. Calculation for Mode Operation with Additional FC Operation

The presence of high oxygen concentration and the subsequent rise in temperature are beneficial for accelerating PM oxidation. Therefore, the important examination is focused on the additional timing required to introduce the mode FC operation. According to the previously outlined formulation, the calculation was conducted to simulate the behavior of soot oxidation-removal under WLTC mode operation. The model must be applied to the oxygen concentration in the exhaust, which fluctuates significantly over short periods of time. As illustrated in Figure 2, the oxygen concentration reaches 20% during the fuel cut (FC) condition, and this high-oxygen period persists for a brief duration, ranging from a few seconds to several seconds. The time conditions for each FC operation were read from a horizontal length (time) in Figure 2 for all cycles. The oxygen concentration was set at 1.0 vol% for the remaining driving cycle. In the research of newly designed FC operation, the total duration of the additional FC was fixed at 100 s and three patterns were examined. A single continuous 100 s FC, three FC events of 30 s, 30 s and 40 s, and five events of 20 s each during the full due course of WLTC were compared with the result of no additional mode. Furthermore, two temperature conditions of 700 °C and 800 °C were set to evaluate the effect of exhaust temperature. They have the potential to make it easier to implement more complex configurations of these FCs.

2.6. Catalytic Reaction and Gas-Phase O₂ Reaction

In practical particulate matter (PM) oxidation processes, two limiting reaction modes are generally considered depending on the contact state between soot and catalyst. One is the solid-state reaction (SSR), in which PM directly contacts the catalyst surface and oxidation proceeds at the catalyst–soot interface. The other is the gas-phase reaction (GPR), where PM that is not in direct contact with the catalyst reacts with gaseous oxygen. In the present model, the PM regeneration process is described as the sum of these two contributions. The kinetic parameters adopted for SSR and GPR are summarized in

Table 1. The frequency factor and activation energy for SSR and GPR.

	Frequency Factor: A	Activation Energy: E [kJ/mol]
SSR	6.2 × 107, 6.2 × 106	100, 120
GPR	2 × 109	195

. For SSR, activation energies and pre-exponential factors were taken from previously reported experimental and modeling studies [21,22,23,24,25,26,27,28,29,33]. For GPR, kinetic parameters were determined from thermogravimetric–differential thermal analysis (TG–DTA) experiments following the procedure described in Ref. [33]. For SSR, activation energies of 105, 110, 115, and 120 kJ/mol were examined. The pre-exponential factor A was set to 6.2 × 10⁷ when the GPF wall was assumed to be fully coated with catalyst, and to 6.2 × 10⁶ when catalyst coverage was incomplete, reflecting reduced effective contact. For GPR, the kinetic parameters were obtained by estimating a shape factor from TG–DTA data.

Soot removal in catalyzed systems involves simultaneous contributions from catalytic oxidation at the soot–catalyst interface and direct oxidation of carbon by oxygen in the gas phase. It is widely recognized that the interaction between soot and the catalyst surface plays a decisive role in the initiation and progression of oxidation. At relatively low temperatures, soot oxidation is initiated predominantly by the catalytic pathway (SSR), while the direct gas-phase oxidation (GPR) becomes increasingly significant as temperature rises. As oxidation proceeds, the soot layer progressively thins, altering the relative contribution of each reaction pathway. The overall soot-removal behavior is governed by temperature, catalyst activity (represented by activation energy), and the physical state of the soot, including its configuration and degree of integration on the substrate surface. Lower activation energy catalysts promote earlier onset of oxidation and higher reaction rates for SSR, thereby reducing the effective soot oxidation temperature.

In this study, activation energy values of 105–120 kJ/mol were selected to represent both currently available catalysts and potential future improvements. Values in the range of 115–120 kJ/mol are consistent with those reported for Pd-based catalysts under practical exhaust conditions [23,24]. More generally, the activation energies employed here fall within ranges reported in previous studies on catalyzed soot oxidation, particularly for ceria-based and noble-metal-supported catalysts under effective soot–catalyst contact conditions [21,22,23,24,25,26,27,28,29]. Lower values (approximately 90–110 kJ/mol) are typically associated with highly active catalytic systems, whereas higher values (≥120 kJ/mol) correspond to more limited oxidation activity under realistic operating conditions.

3. Results

3.1. Effect of Activation Energy on PM Oxidation Performance

This section evaluates the influence of catalyst activity on PM oxidation performance within the GPF, and the limitations of catalyst performance and the necessity of complementary engine control strategies are discussed. Numerical simulations were conducted under four conditions with activation energy (E) set to 100 and 120 kJ/mol, and pre-exponential factor (A) set to 6.2 × 10⁶ and 6.2 × 10⁷, respectively, over one WLTC (1800 s).

The PM inflow rate was set at 0.5 g/h, assuming a total PM introduction of 0.25 g. Figure 4 shows the temporal variation in PM accumulation. The periods from 0 to 600 s, 600–1200 s, and 1200–1800 s correspond to low-speed, medium-speed, and high-speed modes, respectively. The blue solid line represents the case with E = 120 kJ/mol and A = 6.2 × 10⁶; the blue dashed line corresponds to E = 100 kJ/mol and A = 6.2 × 10⁶; the red solid line shows E = 120 kJ/mol and A = 6.2 × 10⁷; and the red dashed line indicates E = 100 kJ/mol and A = 6.2 × 10⁷. Figure 4 illustrates the relationship between activation energy and final PM mass/residual oxidation rate. Red bars represent the remaining PM mass, while black bars show the oxidation rate, calculated using the following formula, based on the initial PM input of 0.25 g:

$$Oxidation rate=\left(1-{\displaystyle \frac{Residual PM}{0.25}}\right)\times 100$$

(10)

In Figure 5, these results indicate that lower activation energy (E) and higher pre-exponential factor (A) promote PM oxidation, reducing the final residual PM. In the case of E = 100 kJ/mol and A = 6.2 × 10⁷, PM accumulation was suppressed even during the low-speed mode, oxidation began during the medium-speed mode (where exhaust temperatures reached 550–600 °C), and combustion was accelerated during the high-speed mode. By the end of the cycle (1800 s), only 0.00299 g of PM remained, corresponding to a high oxidation rate of 98.8%. For E = 100 kJ/mol with A = 6.2 × 10⁶ and E = 120 kJ/mol with A = 6.2 × 10⁷, PM oxidation was insufficient to counterbalance the accumulation during low- and medium-speed phases, resulting in a net increase. However, oxidation overtook accumulation in the latter half of the high-speed phase, where the exhaust temperature exceeded 650 °C, and the residual PM began to decrease. In contrast, under the condition approximating commercially available catalysts (E = 120 kJ/mol, A = 6.2 × 10⁶), though a direct literature reference may be needed, PM oxidation was minimal even during the high-speed mode. As a result, the final PM mass remained at 0.109 g, and the oxidation rate was limited to 56.3%. These findings demonstrate that PM oxidation is highly dependent on catalyst performance. However, in practical applications, installing highly active catalysts is constrained by cost and durability concerns (Figure 5). Therefore, it is necessary to compensate for these limitations through operational control strategies, such as intentionally introducing fuel cut events. The following section quantitatively investigates the effectiveness of forced fuel cuts as a countermeasure.

3.2. Effect of Forced Fuel Cut (FC) on PM Oxidation

This section evaluates the influence of catalyst activity on PM oxidation performance within the GPF and discusses the limitations of catalyst performance and the necessity of complementary engine control strategies. Numerical simulations were conducted under four conditions with activation energy (E) set to 100 and 120 kJ/mol, and pre-exponential factor (A) set to 6.2 × 10⁶ and 6.2 × 10⁷.

In the previous section, we have demonstrated that catalyst performance, represented by parameters such as activation energy and pre-exponential factor, significantly impacts the rate of PM oxidation. However, in practical automotive catalysts, ensuring sufficiently high activity is challenging due to cost, durability, and performance constraints. Therefore, as a compensatory measure for the limitations of catalyst performance, this section investigates the potential of promoting PM oxidation by intentionally introducing fuel-cut (FC) periods, which temporarily raise the oxygen concentration in the exhaust gas.

In this analysis, the PM oxidation behavior in a GPF was evaluated numerically under catalyst conditions of E = 100 kJ/mol and A = 6.2 × 10⁷, focusing on the low-speed phase (0–600 s) of the WLTC mode. The total duration of FC was fixed at 100 s, and three introduction patterns were examined: (1) a single continuous 100 s FC; (2) three divided FC events of 30, 30, and 40 s; and (3) five divided FC events of 20 s each. Two temperature conditions, 700 °C and 800 °C, were also set to evaluate the effect of exhaust temperature.

Figure 6 shows the time-dependent profile of PM accumulation during the low-speed phase of the WLTC. The results clearly indicate that continuous FC significantly suppresses PM buildup compared to split FC or no-FC conditions. In this study, the oxidation rate is evaluated through the temporal evolution of PM mass, where the slope of the PM mass–time profile reflects the balance between PM oxidation and deposition; a steep negative slope indicates accelerated PM oxidation during fuel-cut operation.

When FC was applied continuously for 100 s, the final residual PM mass was 0.010 g at 700 °C and 0.001 g at 800 °C (Figure 7). In contrast, when FC was introduced in three divided intervals, the final residual PM masses were 0.013 g at 700 °C and 0.004 g at 800 °C (Figure 8). For the five-interval case, the values were 0.016 g and 0.009 g, respectively (Figure 9). These results are summarized in

Table 2. PM deposition and residual amount under forced FC introduction conditions (low-speed mode).

Number of FC Installations	Temperature [℃]	Maximum Deposited Volume [g]	Final Residual Volume [g]
1 time (100 s)	700	0.026	0.010
1 time (100 s)	800	0.026	0.001
3 times (30 + 30 + 40 s)	700	0.019	0.013
3 times (30 + 30 + 40 s)	800	0.019	0.004
5 times (20 s × 5)	700	0.016	0.016
5 times (20 s × 5)	800	0.016	0.009

.

By comparing each FC condition with the baseline case (no FC), the improvement in regeneration performance due to FC introduction can be quantitatively assessed. As shown in Figure 6, the PM mass at 600 s under the no-FC condition was 0.0246 g. Using this as a reference, continuous FC for 100 s reduced the final PM mass to 0.001 g, corresponding to a 96% reduction. This substantial PM removal is attributed to the strong acceleration of oxidation reactions caused by the sudden increase in oxygen concentration and sustained heat release.

When FC was divided into three intervals, the final PM mass was 0.004 g, representing an 84% reduction compared to the no-FC case. Although the oxygen supply and heat release effects became intermittent in the divided cases, a high oxidation efficiency was maintained. In the five-interval FC condition, the final PM mass was 0.009 g, corresponding to a 63% reduction. Increasing the number of FC intervals shortens the duration of each event, reducing the sustainability of heat release and local temperature rise, which leads to a diminished regeneration effect. While the oxidation rate varied with each FC strategy, it is also important to consider the peak PM accumulation. Although the final PM mass tended to be slightly higher in the divided FC cases, these strategies effectively suppressed peak PM accumulation. This is advantageous for minimizing pressure drop across the filter and suggests potential for short-cycle partial regeneration strategies. From these results, it is clear that under E = 100 kJ/mol and A = 6.2 × 10⁷ conditions, forced FC significantly enhances PM regeneration. Continuous FC maintains a high-oxygen and elevated-temperature state, which strongly accelerates oxidation reactions and results in the highest PM removal efficiency. Alternatively, divided FC introduces intermittent oxidation, resulting in slightly lower oxidation rates but offering benefits such as suppression of peak PM accumulation. From a physical perspective, the effectiveness of continuous FC can be interpreted in terms of sustained transport enhancement. Similar concepts have been reported in studies on regenerative cooling channels, where continuous flow disturbance and boundary layer disruption promote heat transfer efficiency, whereas intermittent conditions lead to reduced enhancement [35].

In summary, while continuous FC introduction provides the highest PM oxidation efficiency, split FC strategies can effectively mitigate peak PM accumulation and pressure drop. Therefore, the FC strategy must be optimized according to operational conditions and system design goals.

Based on the above findings, forced fuel cut (FC) is effective in promoting PM oxidation, while its effectiveness depends on both temperature conditions and the method of FC introduction. In particular, under low-temperature conditions such as those in the low-speed phase, continuous FC maintains oxidation reactions for a longer duration and leads to a greater regeneration effect.

4. Conclusions

In this study, numerical simulations were conducted from the perspectives of catalyst performance and engine control to improve the regeneration performance of gasoline particulate filters (GPF) under WLTC mode conditions. The main findings are summarized as follows:

• Effect of Catalyst Performance (Activation Energy and Pre-exponential Factor)
  Simulations under four different conditions, varying activation energy (E) and pre-exponential factors (A), revealed that PM oxidation performance highly depends on catalyst activity. Under high-activity conditions (E = 100 kJ/mol, A = 6.2 × 10⁷), an oxidation rate of 98.8% was achieved within a single WLTC, and the final residual PM mass was as low as 0.003 g. In contrast, under conventional catalyst performance (E = 120 kJ/mol, A = 6.2 × 10⁶), oxidation was insufficient, with residual PM reaching 0.11 g, highlighting the limitations in regeneration under such conditions.
• Effectiveness of Forced Fuel Cut (FC) Introduction
  Under conditions of limited catalyst performance, temporarily raising the exhaust oxygen concentration to 20% through forced fuel cut (FC) was shown to promote PM oxidation effectively. This is especially so in the low-speed mode, where exhaust temperatures remain around 500 °C, introducing a single continuous 100 s FC event yielded the highest oxidation effect, reducing PM by approximately 96%. This is attributed to the synergistic effects of sustained oxygen supply and heat release from oxidation reactions, which accelerated and maintained the reaction. On the other hand, when FC was divided into three or five intervals, the oxidation rate slightly decreased, but peak PM accumulation was effectively suppressed. This suggests that a split FC introduction may help reduce pressure drop and improve filter regeneration stability. Therefore, optimizing the FC strategy is crucial to meet multiple performance demands, such as regeneration efficiency and pressure loss reduction, and strategic control tailored to the operating conditions is required.
• Future Issues and Outlook
  The present model analyzed regeneration behavior separately for each speed phase. Future work must include continuous PM accumulation calculations, catalyst aging effects, and exhaust gas fluctuations to more accurately simulate real driving conditions. Moreover, for the practical implementation of forced FC, a comprehensive evaluation of control feasibility, user impact, and safety will be essential.
  Based on the above, the numerical analysis has demonstrated that combining catalyst activity and engine control utilizing fuel cut can effectively improve GPF regeneration performance in GDI vehicles. These findings provide valuable technical insight that may guide the future development of regeneration control algorithms and the design of thermally durable catalysts.