相关论文: A MacCormack Method for Complete Shallow Water Equ…

Mathematical modeling at the level of the full cardiovascular system requires the numerical approximation of solutions to a one-dimensional nonlinear hyperbolic system describing flow in a single vessel. This model is often simulated by…

In this paper, we have used the QUICK scheme of the finite volume method to investigate the problem of steady 2-D free convective incompressible flow with heat and mass transfer in an inclined rectangular domain at different Rayleigh…

In this paper we analyze the use of time splitting techniques for solving shallow water equation. We discuss some properties that these schemes should satisfy so that interactions between the source term and the shock waves are controlled.…

The discontinuous Galerkin finite element method (DGFEM) developed by Rhebergen et al. (2008) offers a robust method for solving systems of nonconservative hyperbolic partial differential equations but, as we show here, does not…

Many numerical schemes for hyperbolic systems require a piecewise polynomial reconstruction of the cell averaged values, and to simulate perturbed steady states accurately we require a so called 'well balanced' reconstruction scheme. For…

In this article, we propose high-order finite-difference entropy stable schemes for the two-fluid relativistic plasma flow equations. This is achieved by exploiting the structure of the equations, which consists of three independent flux…

We introduce a novel artificial compressibility technique to approximate the incompressible Navier-Stokes equations with variable fluid properties such as density and dynamical viscosity. The proposed scheme used the couple pressure and…

In this work, we develop a modelling framework for granular flows based on the shallow water moment equations on inclined planes. Under the assumption of a polynomial expansion of the velocity field, the model extends the classical shallow…

Numerous codes are being developed to solve Shallow Water equations. Because there are used in hydraulic and environmental studies, their capability to simulate properly flow dynamics is critical to guarantee infrastructure and human…

We present a novel approach for solving the shallow water equations using a discontinuous Galerkin spectral element method. The method we propose has three main features. First, it enjoys a discrete well-balanced property, in a spirit…

We consider the coupled system of equations that describe flow in fractured porous media. To describe such types of problems, multicontinuum and multiscale approaches are used. Because in multicontinuum models, the permeability of each…

High-speed turbulent flows are encountered in most space-related applications (including exploration, tourism and defense fields) and represent a subject of growing interest in the last decades. A major challenge in performing high-fidelity…

A few years ago, Bemfica, Disconzi, Noronha, and Kovtun (BDNK) formulated the first causal, stable, strongly hyperbolic, and locally well-posed theory of first-order viscous relativistic hydrodynamics. Since their inception, there have been…

In this paper we consider the numerical solution of the Hamiltonian wave equation in two spatial dimension. We use the Mimetic Finite Difference (MFD) method to approximate the continuous problem combined with a symplectic integration in…

By reduction to a generalized Sturm Liouville problem, we establish spectral stability of hydraulic shock profiles of the Saint-Venant equations for inclined shallow-water flow, over the full parameter range of their existence, for both…

We present a numerical method for studying the normal modes of accretion flows around black holes. In this first paper, we focus on two-dimensional, viscous, hydrodynamic disks, for which the linear modes have been calculated analytically…

We propose, analyze, and test a penalty projection-based efficient and accurate algorithm for the Uncertainty Quantification (UQ) of the time-dependent Magnetohydrodynamic (MHD) flow problems in convection-dominated regimes. The algorithm…

This paper describes the first steps of development of a new multidimensional time implicit code devoted to the study of hydrodynamical processes in stellar interiors. The code solves the hydrodynamical equations in spherical geometry and…

A semi-implicit two-phase double-point Material Point Method (MPM) formulation, based on the incremental fractional-step method to model large deformation geotechnical problems has been derived. The semi-implicit formulation has two…

We propose a new family of high order staggered semi-implicit discontinuous Galerkin (DG) methods for the simulation of natural convection problems. Assuming small temperature fluctuations, the Boussinesq approximation is valid and the flow…