相关论文: A hybrid WENO method with modified ghost fluid met…

In this paper, we are concerned with the shallow water flow model over non-flat bottom topography by high-order schemes. Most of the numerical schemes in the literature are developed from the original mathematical model of the shallow water…

This article reports on the efficiency of a co-located diffuse approximation method coupled with a projection algorithm for the solution of two and three-dimensional incompressible flow equations. Three typical examples show the accuracy of…

Simulating the flow of two fluid phases in porous media is a challenging task, especially when fractures are included in the simulation. Fractures may have highly heterogeneous properties compared to the surrounding rock matrix,…

The majority of available numerical algorithms for interfacial two-phase flows either treat both fluid phases as incompressible (constant density) or treat both phases as compressible (variable density). This presents a limitation for the…

This paper presents a fully multidimensional kernel-based reconstruction scheme for finite volume methods applied to systems of hyperbolic conservation laws, with a particular emphasis on the compressible Euler equations. Non-oscillatory…

In this study, we introduce a tensor-train (TT) finite difference WENO method for solving compressible Euler equations. In a step-by-step manner, the tensorization of the governing equations is demonstrated. We also introduce…

In this paper, a simple and efficient third-order weighted essentially non-oscillatory (WENO) reconstruction is developed for three-dimensional flows, in which the idea of two-dimensional WENO-AO scheme on unstructured meshes…

We present a novel high order semi-implicit hybrid finite volume/virtual element numerical scheme for the solution of compressible flows on Voronoi tessellations. The method relies on the flux splitting of the compressible Navier-Stokes…

In this paper, a high order implicit Method of Line Transpose (MOL$^T$ ) method based on a weighted essentially non-oscillatory (WENO) methodology is developed for one-dimensional linear transport equations and further applied to the…

The aim of the present paper is to provide a comparison between several finite-volume methods of different numerical accuracy: second-order Godunov method with PPM interpolation and high-order finite-volume WENO method. The results show…

We present and compare third- as well as fifth-order accurate finite difference schemes for the numerical solution of the compressible ideal MHD equations in multiple spatial dimensions. The selected methods lean on four different…

This paper presents a generalized ENO (GENO)-type nonlinear reconstruction scheme for compressible flow simulations. The proposed reconstruction preserves the accuracy of the linear scheme while maintaining essentially non-oscillatory…

In this paper, we extend the previous work on absolutely convergent fixed-point fast sweeping WENO methods by Li et al. (J. Comput. Phys. 443: 110516, 2021) and design a fifth-order hybrid fast sweeping scheme for solving steady state…

In this paper, we present a multi-dimensional, arbitrary-order hybrid reconstruction framework for compressible flows on unstructured meshes. The method combines the efficiency of linear reconstruction with the robustness of high-order…

The volume of fluid (VoF) method is widely used in multi-phase flow simulations to track and locate the interface between two immiscible fluids. A major bottleneck of the VoF method is the interface reconstruction step due to its high…

In subsurface multiphase flow simulations, poor nonlinear solver performance is a significant runtime sink. The system of fully implicit mass balance equations is highly nonlinear and often difficult to solve for the nonlinear solver,…

Steady state simulations} of magnetized electron fluid equations with strong anisotropic diffusion based on the first-order hyperbolic approach is carried out using cell-centered higher order upwind schemes, linear and weighted essentially…

In this paper, a meshfree method using physics-informed neural networks (PINNs) is developed for solving two-phase flow problems with moving interfaces, where two immiscible fluids bearing different material properties, are separated by a…

A two-phase, low-Mach-number flow solver is created and verified for variable-density liquid and gas with phase change. The interface is sharply captured using a split Volume-of-Fluid method generalized for a non-divergence-free liquid…

Higher order finite difference Weighted Essentially Non-Oscillatory (WENO) schemes for conservation laws represent a technology that has been reasonably consolidated. They are extremely popular because, when applied to multidimensional…