Search Results (24)

This paper proposes a global, predefined time control method based on a predefined time disturbance observer to address the issues of wide flight airspace, large aerodynamic deviations, and high precision requirements for the entire process of aerospace aircraft re-entry. Firstly, this method proposes an adjustable predefined time nonsingular sliding mode disturbance observer, which can not only accurately estimate the modeling uncertainty and external aerodynamic disturbances of the aerospace aircraft, but also quickly converge while suppressing chattering. Then, based on the disturbance observation results, combined with a new performance function and nonsingular predefined-time sliding mode, a global predefined-time controller suitable for any order system was designed. Unlike existing methods that can only ensure that the initial deviation converges to the deviation boundary within a predefined time and then remains within the deviation boundary, it can ensure that any deviation generated within the error boundary also converges within the predefined time. Finally, the effectiveness and superiority of the proposed control scheme were verified through comparative simulation. Full article

Numerical solutions of turbulent mass-transfer diffusion present challenges due to the nonlinearity of the elliptic–parabolic degeneracy of the mathematical models. Our main result in this paper concerns the development and implementation of an efficient high-order numerical method that is fourth-order accurate in space and second-order accurate in time for computing both the solution and its gradient for a Barenblatt-type equation. First, we reduce the original Neumann boundary value problem to a Dirichlet problem for the equation of the solution gradient. This problem is then solved by a compact fourth-order spatial approximation. To implement the numerical discretization, we employ Newton’s iterative method. Then, we compute the original solution while preserving the order of convergence. Numerical test results confirm the efficiency and accuracy of the proposed numerical scheme. Full article

This study investigates the effectiveness of the large eddy simulation version of the Weather Research and Forecasting model (WRF-LES) in reproducing the atmospheric conditions observed during a Perdigão field experiment. When comparing the results of the WRF-LES with observations, using LES settings can accurately represent both large-scale events and the specific characteristics of atmospheric circulation at a small scale. Six sensitivity experiments are performed to evaluate the impact of different planetary boundary layer (PBL) schemes, including the MYNN, YSU, and Shin and Hong (SH) PBL models, as well as large eddy simulation (LES) with Smagorinsky (SMAG), a 1.5-order turbulence kinetic energy closure (TKE) model, and nonlinear backscatter and anisotropy (NBA) subgrid-scale (SGS) stress models. Two case studies are selected to be representative of flow conditions. In the northeastern flow, the MYNN NBA simulation yields the best result at a height of 100 m with an underestimation of 3.4%, despite SH generally producing better results than PBL schemes. In the southwestern flow, the MYNN TKE simulation at station Mast 29 is the best result, with an underestimation of 1.2%. The choice of SGS models over complex terrain affects wind field features in the boundary layer more than above the boundary layer. The NBA model generally produces better results in complex terrain when compared to other SGS models. In general, the WRF-LES can model the observed flow with high-resolution topographic maps in complex terrain with different SGS models for both flow regimes. Full article

We extend the 3D Lattice Boltzmann method with a deformable boundary (LBM-DB) for the computations of the full-volume colonic flow of the Newtonian fluid driven by the peristaltic segmented circular contractions which obey the three-step “intestinal law”: (i) deflation, (ii) inflation, and (iii) elastic relaxation. The key point is that the LBM-DB accurately prescribes a curved deforming surface on the regular computational grid through precise and compact Dirichlet velocity schemes, without the need to recover for an adaptive boundary mesh or surface remesh, and without constraint of fluid volume conservation. The population “refill” of “fresh” fluid nodes, including sharp corners, is reformulated with the improved reconstruction algorithms by combining bulk and advanced boundary LBM steps with a local sub-iterative collision update. The efficient parallel LBM-DB simulations in silico then extend the physical experiments performed in vitro on the Dynamic Colon Model (DCM, 2020) to highly occlusive contractile waves. The motility scenarios are modeled both in a cylindrical tube and in a new geometry of “parabolic” transverse shape, which mimics the dynamics of realistic triangular lumen aperture. We examine the role of cross-sectional shape, motility pattern, occlusion scenario, peristaltic wave speed, elasticity effect, kinematic viscosity, inlet/outlet conditions and numerical compressibility on the temporal localization of pressure and velocity oscillations, and especially the ratio of retrograde vs antegrade velocity amplitudes, in relation to the major contractile events. The developed numerical approach could contribute to a better understanding of the intestinal physiology and pathology due to a possibility of its straightforward extension to the non-Newtonian chyme rheology and anatomical geometry. Full article

To achieve high-fidelity large eddy simulation (LES) predictions of complex flows while keeping computational costs manageable, this study integrates a high-order WENO-ZQ scheme into the LES framework. The WENO-ZQ scheme has been extensively studied for its accuracy, robustness, and computational cost in inviscid flow applications. This study extended the WENO-ZQ scheme to viscous flows by integrating it into a three-dimensional structured grid LES CFD solver. High-fidelity simulations of turbulent boundary layer flow and supersonic compression ramp flows were conducted, with the scheme being applied for the first time to study laminar boundary layer transition and separation flows in the high-load, low-pressure turbine PakB cascade. Classic numerical case validations for viscous conditions demonstrate that the WENO-ZQ scheme, compared to the same-order WENO-JS scheme, exhibits lower dispersion and dissipation errors, faster convergence, and better high-frequency wave resolution. It maintains high-resolution accuracy with fewer grid points. In application cases, the WENO-ZQ scheme accurately captures the three-dimensional flow characteristics of shockwave–boundary layer interactions in supersonic compression ramps and shows high accuracy and resolution in predicting separation and separation-induced transition in low-pressure turbines. Full article

In this article, a numerical method is proposed and investigated for an initial boundary value problem governed by a fractional differential generalization of the nonlinear transient filtration law which describes fluid motion in a porous medium. This type of equation is widely used to describe complex filtration processes such as fluid movement in horizontal wells in fractured geological formations. To construct the numerical method, a high-order approximation formula for the fractional derivative in the sense of Caputo is applied, and a combination of the finite difference method with the finite element method is used. The article proves the uniqueness and continuous dependence of the solution on the input data in differential form, as well as the stability and convergence of the proposed numerical scheme. The linearization of nonlinear terms is carried out by the Newton method, which allows for achieving high accuracy in solving complex problems. The research results are confirmed by a series of numerical tests that demonstrate the applicability of the developed method in real engineering problems. The practical significance of the presented approach lies in its ability to accurately and effectively model filtration processes in shale formations, which allows engineers and geologists to make more informed decisions when designing and operating oil fields. Full article

As open channel simulations are of great economic and human significance, many numerical approaches have been developed, with the Godunov schemes showing particular promise. To evaluate, confirm, and extend the simulation results of others, a variety of first- and second-order FVMs are available, with Rusanov and Roe schemes being used here to simulate the demanding case of 1D and 2D flows following a dam break. The virtual boundary cells approach is shown to achieve a monotonic solution for both interior and boundary cells, and while flux computation is employed at boundary cells, a refinement is only rarely used in existing models. A number of variations are explored, including the TVD MUSCL-Hancock (monotone upwind scheme for conservation laws) numerical scheme with several slope limiters in a quest to avoid spurious oscillations. The sensitivity of the results to both channel length and the ratio of downstream to initial upstream water depth is explored using 1D and 2D models. The Roe scheme with a Van Leer limiter as a slope limiter is shown to be both fast and slightly more accurate than other slope limiters for this problem, but the Rusanov scheme with different slope limiters works well for 1D simulations. Significantly, the selection of an appropriate slope limiter is shown to be best based on the ratio of the downstream to upstream water depth. However, this study focuses on the special case where the ratio of the initial depth downstream to upstream of the dam is equal to or less than 0.5, and these outcomes are compared to theoretical results. The 2D dam-break problem is used to further explore first- and second-order methods using different slope limiters, and the results show that the Superbee limiter can be problematic due to an observed large dispersion in depth contours. However, the most promising approaches from previous studies are confirmed to deserve the high regard given to them by many researchers. Full article

This article is devoted to the study of high-order, accurate difference schemes’ numerical solutions of local and non-local problems for ordinary differential equations of the fourth order. Local and non-local problems for ordinary differential equations with constant coefficients can be solved by classical integral transform methods. However, these classical methods can be used simply in the case when the differential equation has constant coefficients. We study fourth-order differential equations with dependent coefficients and their corresponding boundary value problems. Novel compact numerical solutions of high-order, accurate finite difference schemes generated by Taylor’s decomposition on five points have been studied in these problems. Numerical experiments support the theoretical statements for the solution of these difference schemes. Full article

Unsteady separation is a phenomenon that occurs in many flows and results in increased drag, decreased lift, noise emission, and loss of efficiency or failure in flow devices. Turbulence models for the steady or unsteady Reynolds-averaged Navier–Stokes equations (RANS and URANS, respectively) are commonly used in industry; however, their performance is often unsatisfactory. The comparison of RANS results with experimental data does not clearly isolate the modeling errors, since differences with the data may be due to a combination of modeling and numerical errors, and also to possible differences in the boundary conditions. In the present study, we use high-fidelity large-eddy simulation (LES) results to carry out a consistent evaluation of the turbulence models. By using the same numerical scheme and boundary conditions as the LES, and a grid on which grid convergence was achieved, we can isolate modeling errors. The calculations (both LES and RANS) are carried out using a well-validated, second-order-accurate code. Separation is generated by imposing a freestream velocity distribution, that is modulated in time. We examined three frequencies (a rapid, flutter-like oscillation, an intermediate one in which the forcing and the flow have the same timescales, and a quasi-steady one). We also considered three different pressure distributions, one with alternating favorable and adverse pressure gradients (FPGs and APGs, respectively), one oscillating between an APG and a zero-pressure gradient (ZPG), and one with an oscillating APG. All turbulence models capture the general features of this complex unsteady flow as well or better than in similar steady cases. The presence, during the cycle, of times in which the freestream pressure-gradient is close to zero affects significantly the model performance. Comparing our results with those in the literature indicates that numerical errors due to the type of discretization and the grid resolution are as significant as those due to the turbulence model. Full article

The trade-off between numerical accuracy and computational cost is always an important factor to consider when pricing options numerically, due to the inherent irregularity and existence of non-linearity in many models. In this work, we first present fast and accurate (1,2) and (2,2) predictor–corrector methods with a fourth-order compact finite difference scheme for pricing coupled system of the non-linear free boundary option pricing problem consisting of the option value and delta sensitivity. To predict the optimal exercise boundary, we set up a high-order boundary scheme, which is strategically derived using a combination of the fourth-order Robin boundary scheme and the fourth-order compact finite difference scheme near boundary. Furthermore, we implement a three-step high-order correction scheme for computing interior values of the option value and delta sensitivity. The discrete matrix system of this correction scheme has a tri-diagonal structure and strictly diagonal dominance. This nice feature allows for the implementation of the Thomas algorithm, thereby enabling fast computation. The optimal exercise boundary value is also corrected in each of the three correction steps with the derived Robin boundary scheme. Our implementations are fast on both coarse and very refined grids and provide highly accurate numerical approximations. Moreover, we recover a reasonable convergence rate. Further extensions to high-order predictor two-step corrector schemes are elaborated. Full article

This study deals with the numerical solution of a class of linear systems of second-order boundary value problems (BVPs) using a new symmetric cubic B-spline method (NCBM). This is a typical cubic B-spline collocation method powered by new approximations for second-order derivatives. The flexibility and high order precision of B-spline functions allow them to approximate the answers. These functions have a symmetrical property. The new second-order approximation plays an important role in producing more accurate results up to a fifth-order accuracy. To verify the proposed method’s accuracy, it is tested on three linear systems of ordinary differential equations with multiple step sizes. The numerical findings by the present method are quite similar to the exact solutions available in the literature. We discovered that when the step size decreased, the computational errors decreased, resulting in better precision. In addition, details of maximum errors are investigated. Moreover, simple implementation and straightforward computations are the main advantages of the offered method. This method yields improved results, even if it does not require using free parameters. Thus, it can be concluded that the offered scheme is reliable and efficient. Full article

The boundary conditions are crucial for numerical methods. This study aims to contribute to this growing area of research by exploring boundary conditions for the discrete unified gas kinetic scheme (DUGKS). The importance and originality of this study are that it assesses and validates the novel schemes of the bounce back (BB), non-equilibrium bounce back (NEBB), and Moment-based boundary conditions for the DUGKS, which translate boundary conditions into constraints on the transformed distribution functions at a half time step based on the moment constraints. A theoretical assessment shows that both present NEBB and Moment-based schemes for the DUGKS can implement a no-slip condition at the wall boundary without slip error. The present schemes are validated by numerical simulations of Couette flow, Poiseuille flow, Lid-driven cavity flow, dipole–wall collision, and Rayleigh–Taylor instability. The present schemes of second-order accuracy are more accurate than the original schemes. Both present NEBB and Moment-based schemes are more accurate than the present BB scheme in most cases and have higher computational efficiency than the present BB scheme in the simulation of Couette flow at high Re. The present Moment-based scheme is more accurate than the present BB, NEBB schemes, and reference schemes in the simulation of Poiseuille flow and dipole–wall collision, compared to the analytical solution and reference data. Good agreement with reference data in the numerical simulation of Rayleigh–Taylor instability shows that they are also of use to the multiphase flow. The present Moment-based scheme is more competitive in boundary conditions for the DUGKS. Full article

High-precision finite difference (FD) wavefield simulation is one of the key steps for the successful implementation of full-waveform inversion and reverse time migration. Most explicit FD schemes for solving seismic wave equations are not compact, which leads to difficulty and low efficiency in boundary condition treatment. Firstly, we review a family of tridiagonal compact FD (CFD) schemes of various orders and derive the corresponding optimization schemes by minimizing the error between the true and numerical wavenumber. Then, the optimized CFD (OCFD) schemes and a second-order central FD scheme are used to approximate the spatial and temporal derivatives of the 2D acoustic wave equation, respectively. The accuracy curves display that the CFD schemes are superior to the central FD schemes of the same order, and the OCFD schemes outperform the CFD schemes in certain wavenumber ranges. The dispersion analysis and a homogeneous model test indicate that increasing the upper limit of the integral function helps to reduce the spatial error but is not conducive to ensuring temporal accuracy. Furthermore, we examine the accuracy of the OCFD schemes in the wavefield modeling of complex structures using a Marmousi model. The results demonstrate that the OCFD4 schemes are capable of providing a more accurate wavefield than the CFD4 scheme when the upper limit of the integral function is 0.5π and 0.75π. Full article

In this study, a high-order compact finite difference method is used to solve boundary value problems with Robin boundary conditions. The norm is to use a first-order finite difference scheme to approximate Neumann and Robin boundary conditions, but that compromises the accuracy of the entire scheme. As a result, new higher-order finite difference schemes for approximating Robin boundary conditions are developed in this work. Six examples for testing the applicability and performance of the method are considered. Convergence analysis is provided, and it is consistent with the numerical results. The results are compared with the exact solutions and published results from other methods. The method produces highly accurate results, which are displayed in tables and graphs. Full article

The water hammer phenomenon is the main problem in long-distance pipeline networks. The MOC (Method of characteristics) and finite difference methods lead to severe constraints on the mesh and Courant number, while the finite volume method of the second-order Godunov scheme has limited intermittent capture capability. These methods will produce severe numerical dissipation, affecting the computational efficiency at low Courant numbers. Based on the lax-Friedrichs flux splitting method, combined with the upstream and downstream virtual grid boundary conditions, this paper uses the high-precision fifth-order WENO scheme to reconstruct the interface flux and establishes a finite volume numerical model for solving the transient flow in the pipeline. The model adopts the GPU parallel acceleration technology to improve the program’s computational efficiency. The results show that the model maintains the excellent performance of intermittent excitation capture without spurious oscillations even at a low Courant number. Simultaneously, the model has a high degree of flexibility in meshing due to the high insensitivity to the Courant number. The number of grids in the model can be significantly reduced and higher computational efficiency can be obtained compared with MOC and the second-order Godunov scheme. Furthermore, this paper analyzes the acceleration effect in different grids. Accordingly, the acceleration effect of the GPU technique increases significantly with the increase in the number of computational grids. This model can support efficient and accurate fast simulation and prediction of non-constant transient processes in long-distance water pipeline systems. Full article