Search Results (100)

As the development of offshore wind energy transforms from coastal to deep-sea regions, designing a cost effective mooring system while ensuring the safety of floating offshore wind turbine (FOWT) remains a critical challenge, especially considering extreme wave environments. This study employs a model coupling computational fluid dynamics (CFD) and finite element method (FEM) to investigate the responses of a parked FOWT platform with its mooring system under rogue wave conditions. Specifically, the mooring dynamics are solved using a local discontinuous Galerkin (LDG) method, which is believed to provide high accuracy. Firstly, rogue wave generation and the coupled CFD-FEM are validated through comparisons with existing experimental and numerical data. Secondly, FOWT platform motions and mooring tensions caused by a rogue wave are obtained through simulations, which are compared with the ones caused by a similar peak-clipped rogue wave. Lastly, analysis of four different mooring design schemes is conducted to evaluate their performance on reducing the mooring tensions. The results indicate that the rogue wave leads to significantly enlarged FOWT platform motions and mooring tensions, while doubling the number of mooring lines with specific line angles provides the most balanced performance considering cost-effectiveness and structural safety under identical rogue wave conditions. Full article

This study presents high-fidelity numerical simulations of the shock-accelerated single-mode Richtmyer–Meshkov instability (RMI) in a light helium layer confined between two interfaces and surrounded by nitrogen gas. A high-order modal discontinuous Galerkin method is employed to solve the two-dimensional compressible Euler equations, enabling detailed investigation of interface evolution, vorticity dynamics, and flow structure development under various physical conditions. The effects of helium layer thickness, initial perturbation amplitude, and incident shock Mach number are systematically explored by analyzing interface morphology, vorticity generation, enstrophy, and kinetic energy. The results show that increasing the helium layer thickness enhances vorticity accumulation and interface deformation by delaying interaction with the second interface, allowing more sustained instability growth. Larger initial perturbation amplitudes promote earlier onset of nonlinear deformation and stronger baroclinic vorticity generation, while higher shock strengths intensify pressure gradients across the interface, accelerating instability amplification and mixing. These findings highlight the critical interplay between layer confinement, perturbation strength, and shock strength in governing the nonlinear evolution of RMI in light fluid layers. Full article

Accurately modeling fractures in wave-propagation simulations is challenging due to their small scale relative to other features. While equivalent-media models can approximate fracture-induced anisotropy, they fail to capture their discrete influence on wave propagation. To address this limitation, the Interior-Penalty Discontinuous Galerkin Method (IP-DGM) can be adapted to incorporate the Linear-Slip Model (LSM) to represent fractures explicitly. In this study, we apply IP-DGM to elastic wave propagation in fractured cylindrical domains using realistic fracture compliances obtained from laboratory experiments (using ultrasonic-pulse transmission) to simulate the effects of fluid-filled fractures. We analyze how fracture spacing and fluid type influence P- and S-wave behavior, focusing on amplitude attenuation and wave-front delays. Our numerical results align with experimental and theoretical predictions, demonstrating that higher-density fluids enhance wave transmission, reducing the impedance contrast and improving coupling across fracture surfaces. These findings highlight the capability of IP-DGM to accurately model wave propagation in realistic fractured and saturated media, providing a valuable tool for seismic monitoring in fractured reservoirs and other applications where fluid-filled fractures are prevalent. Full article

In this paper, a structure-preserving local discontinuous Galerkin (LDG) method is proposed for parabolic stochastic partial differential equations with periodic boundary conditions and multiplicative noise. It is proven that under certain conditions, this numerical method is stable in the $L^2$ sense and can preserve energy conservation. The optimal spatial error estimate in the mean square sense can reach $n+1$ if the degree of the polynomial is n. The correctness of the theoretical results is verified through numerical examples. Full article

Godunov-based finite volume (FV) methods are widely employed to numerically solve the Shallow-Water Equations (SWEs) with application to simulate flood inundation over irregular geometries and real-field, where unstructured triangular meshing is favored. Second-order extensions have been devised, mostly on the MUSCL reconstruction and the discontinuous Galerkin (DG) approaches. In this paper, we introduce a novel second-order Runge–Kutta discontinuous Galerkin (RKDG) solver for flood modeling, specifically addressing positivity preservation and wetting and drying on unstructured triangular meshes. To enhance the RKDG model, we adapt and refine positivity-preserving and wetting and drying techniques originally developed for the MUSCL-based finite volume (FV) scheme, ensuring its effective integration within the RKDG framework. Two analytical test problems are considered first to validate the proposed model and assess its performance in comparison with the MUSCL formulation. The performance of the model is further explored in real flooding scenarios involving irregular topographies. Our findings indicate that the added complexity of the RKDG model is justified, as it delivers higher-quality results even on very coarse meshes. This reveals that there is a promise in deploying RKDG-based flood models in real-scale applications, in particular when field data are sparse or of limited resolution. Full article

In numerical simulations of underwater explosions, inaccuracies in the parameters of the Jones–Wilkins–Lee (JWL) equation of state often result in significant deviations between predicted shock wave pressure peaks or bubble pulsation periods and experimental or empirical results. To achieve the precise forecasting of underwater explosion loads, a corrected method for adjusting the initial conditions of explosives is proposed. This method regulates explosion loads by correcting the initial density and initial internal energy per unit mass of the explosive, offering a straightforward implementation and easy extension to complex scenarios. In addition, the accuracy and feasibility of the proposed method were validated through comparisons with experimental data and empirical formulas from international studies. The numerical framework employs the Runge–Kutta Discontinuous Galerkin (RKDG) method to solve the one-dimensional Euler equations. The spatial discretization of the Euler domain is achieved using the discontinuous Galerkin (DG) method, while temporal discretization utilizes a third-order Runge–Kutta (RK) method. The results demonstrate that the proposed correction method effectively compensates for load discrepancies caused by inaccuracies in the JWL equation of state parameters. After correction, the maximum error in the shock wave pressure peak is reduced to less than 4.5%, and the maximum error in the bubble pulsation period remains below 1.9%. Full article

Solving the Euler equations often requires expensive computations of complex, high-order time derivatives. Although Taylor Discontinuous Galerkin (TDG) schemes are renowned for their accuracy and stability, directly evaluating third-order tensor derivatives can significantly reduce computational efficiency, particularly for large-scale, intricate flow problems. To overcome this difficulty, this paper presents an optimized numerical procedure that combines Taylor series time integration with the Discontinuous Galerkin (DG) approach. By replacing cumbersome tensor derivatives with simpler time derivatives of the Jacobian matrix and finite difference method inside the element to calculate the high-order time derivative terms, the proposed method substantially decreases the computational cost while maintaining accuracy and stability. After verifying its fundamental feasibility in one-dimensional tests, the optimized TDG method is applied to a two-dimensional forward-facing step problem. In all numerical tests, the optimized TDG method clearly exhibits a computational efficiency advantage over the conventional TDG method, therefore saving a great amount of time, nearly 70%. This concept can be naturally extended to higher-dimensional scenarios, offering a promising and efficient tool for large-scale computational fluid dynamics simulations. Full article

The current research study presents a comprehensive analysis of the local discontinuous Galerkin (LDG) method for solving multi-order fractional differential equations (FDEs), with an emphasis on circuit modeling applications. We investigated the existence, uniqueness, and numerical stability of LDG-based discretized formulation, leveraging the Liouville–Caputo fractional derivative and upwind numerical fluxes to discretize governing equations while preserving stability. The method was validated through benchmark test cases, including comparisons with analytical solutions and established numerical techniques (e.g., Gegenbauer wavelets and Dickson collocation). The results demonstrate that the LDG method achieves high-accuracy solutions (e.g., with a relatively large time step size) and reduced computational costs, which are attributed to its element-wise formulation. These findings position LDG as a promising tool for complex scientific and engineering applications, particularly in modeling fractional-order systems such as RL, RLC circuits, and other electrical circuit equations. Full article

This work develops a novel two-dimensional, depth-integrated, non-hydrostatic model for wave propagation simulation using a weighted average non-hydrostatic pressure profile. The model is constructed by modifying an existing non-hydrostatic discontinuous/continuous Galerkin finite-element model with a linear, vertical, non-hydrostatic pressure profile. Using a weighted average linear/quadratic non-hydrostatic pressure profile has been shown to increase the performance of earlier models. The results suggest that implementing a weighted average non-hydrostatic pressure profile, in conjunction with a calculated or optimized $Ө$ weight parameter, improves the dispersion characteristics of depth-integrated, non-hydrostatic models in shallow and intermediate water depths. A series of analytical solutions and data from previous laboratory experiments verify and validate the model. Full article

As an effective geophysical tool, ground penetrating radar (GPR) is widely used for environmental and engineering detections. Numerous numerical simulation algorithms have been developed to improve the computational efficiency of GPR simulations, enabling the modeling of complex structures. The discontinuous Galerkin method is a high efficiency numerical simulation algorithm which can deal with complex geometry. This method uses numerical fluxes to ensure the continuity between elements, allowing Maxwell’s equations to be solved within each element without the need to assemble a global matrix or solve large systems of linear equations. As a result, memory consumption can be significantly reduced, and parallel solvers can be applied at the element level, facilitating the construction of high-order schemes to enhance computational accuracy. In this paper, we apply the discontinuous Galerkin (DG) method based on unstructured meshes to 3D GPR simulation. To verify the accuracy of our algorithm, we simulate a full-space vacuum and a cuboid in a homogeneous medium and compare results, respectively, with the analytical solutions and those from the finite-difference method. The results demonstrate that, for the same error level, the proposed DG method has significant advantages over the FDTD method, with less than 20% of the memory consumption and calculation time. Additionally, we evaluate the effectiveness of our method by simulating targets in an undulating subsurface, and further demonstrate its capability for simulating complex models. Full article

This study computationally examined the Richtmyer–Meshkov instability (RMI) evolution in a helium backward-triangular bubble immersed in monatomic argon, diatomic nitrogen, and polyatomic methane under planar shock wave interactions. Using high-fidelity numerical simulations based on the compressible Navier–Fourier equations based on the Boltzmann–Curtiss kinetic framework and simulated via a modal discontinuous Galerkin scheme, we analyze the complex interplay of shock-bubble dynamics. Key findings reveal distinct thermal non-equilibrium effects, vorticity generation, enstrophy evolution, kinetic energy dissipation, and interface deformation across gases. Methane, with its molecular complexity and higher viscosity, exhibits the highest levels of vorticity production, enstrophy, and kinetic energy, leading to pronounced Kelvin–Helmholtz instabilities and enhanced mixing. Conversely, argon, due to its simpler atomic structure, shows weaker deformation and mixing. Thermal non-equilibrium effects, quantified by the Rayleigh–Onsager dissipation function, are most significant in methane, indicating delayed energy relaxation and intense turbulence. This study highlights the pivotal role of molecular properties, specific heat ratio, and bulk viscosity in shaping RMI dynamics in polyatomic gases, offering insights on uses such as high-speed aerodynamics, inertial confinement fusion, and supersonic mixing. Full article

This paper presents a novel parallel-GPU discontinuous Galerkin time domain (DGTD) method with a third-order local time stepping (LTS) scheme for the solution of multi-scale electromagnetic problems. The parallel-GPU implementations were developed based on NVIDIA’s recommendations to guarantee the optimal GPU performance, and an LTS scheme based on the third-order Runge–Kutta (RK3) method was used to accelerate the solution of multi-scale problems further. This LTS scheme used third-order interpolation polynomials to ensure the continuity of the time solution. The numerical results indicate that the strategy with the parallel-GPU DGTD and LTS maintains the order of precision of standard global time stepping (GTS) and reduces the execution time by about 78% for a complex multi-scale electromagnetic scattering problem. Full article

This article presents a comparison between the performance obtained by using a spatial discretization of the Euler equations based on a high-order discontinuous Galerkin (dG) method and different sets of variables. The sets of variables investigated are as follows: (1) conservative variables; (2) primitive variables based on pressure and temperature; (3) primitive variables based on the logarithms of pressure and temperature. The solution is advanced in time by using a linearly implicit high-order Rosenbrock-type scheme. The results obtained using the different sets are assessed across several canonical unsteady test cases, focusing on the accuracy, conservation properties and robustness of each discretization. In order to cover a wide range of physical flow conditions, the test-cases considered here are (1) the isentropic vortex convection, (2) the Kelvin–Helmholtz instability and (3) the Richtmyer–Meshkov instability. Full article

The Mach number effect on the Richtmyer–Meshkov instability (RMI) evolution of the shocked V-shaped ${\mathrm{N}}_2$/${\mathrm{SF}}_6$ interface is numerically studied in this research. Four distinct Mach numbers are taken into consideration for this purpose: ${\mathrm{M}}_s=1.12,1.22,1.42$, and 1.62. A two-dimensional space of compressible two-component Euler equations is simulated using a high-order modal discontinuous Galerkin approach to computational simulations. The numerical results show good consistency when compared to the available experimental data. The computational results show that the RMI evolution in the shocked V-shaped ${\mathrm{N}}_2$/${\mathrm{SF}}_6$ interface is critically dependent on the Mach number. The flow field, interface deformation, intricate wave patterns, inward jet development, and vorticity generation are all strongly impacted by the shock Mach number. As the Mach number increases, the V-shaped interface deforms differently, and the distance between the Mach stem and the triple points varies depending on the Mach number. Compared to lower Mach numbers, higher ones produce larger rolled-up vortex chains. A thorough analysis of the Mach number effect identifies the factors that propel the creation of vorticity during the interaction phase. Moreover, kinetic energy and enstrophy both dramatically rise with increasing Mach number. Lastly, a detailed analysis is carried out to determine how the Mach number affects the temporal variations in the V-shaped interface’s features. Full article

This paper investigates numerically the shock wave interaction with a V-shaped heavy/light interface. For numerical simulations, we choose six distinct vertex angles ($\theta ={40}^{\circ },{60}^{\circ },{90}^{\circ },{120}^{\circ },{150}^{\circ }$, and ${170}^{\circ })$, five distinct shock wave strengths (${\mathrm{M}}_s=1.12,1.22,1.30,1.60,$ and $2.0$), and three different Atwood numbers ($At=-0.32,-0.77,$ and $-0.87$). A two-dimensional space of compressible two-component Euler equations are solved using a third-order modal discontinuous Galerkin approach for the simulations. The present findings demonstrate that the vertex angle has a crucial influence on the shock wave interaction with the V-shaped heavy/light interface. The vertex angle significantly affects the flow field, interface deformation, wave patterns, spike generation, and vorticity production. As the vertex angle decreases, the vorticity production becomes more dominant. A thorough analysis of the vertex angle effect identifies the factors that propel the creation of vorticity during the interaction phase. Notably, smaller vertex angles lead to stronger vorticity generation due to a steeper density gradient, while larger angles result in weaker, more dispersed vorticity and a less complex interaction. Moreover, kinetic energy and enstrophy both dramatically rise with decreasing vortex angles. A detailed analysis is also carried out to analyze the vertex angle effects on the temporal variations of interface features. Finally, the impacts of different Mach and Atwood numbers on the V-shaped interface are briefly presented. Full article