相关论文: A Positivity-preserving High Order Finite Volume C…

We present an implicit-explicit finite volume scheme for the Euler equations. We start from the non-dimensionalised Euler equations where we split the pressure in a slow and a fast acoustic part. We use a Suliciu type relaxation model which…

We propose an alternative reconstruction for weighted essentially non-oscillatory schemes with adaptive order (WENO-AO) for solving hyperbolic conservation laws. The alternative reconstruction has a more concise form than the original…

This paper proposes and analyzes a novel efficient high-order finite volume method for the ideal magnetohydrodynamics (MHD). As a distinctive feature, the method simultaneously preserves a discretely divergence-free (DDF) constraint on the…

In this paper we develop a new sixth-order finite difference central weighted essentially non-oscillatory (WENO) scheme with Z-type nonlinear weights for nonlinear degenerate parabolic equations. The centered polynomial is introduced for…

The high-order Target ENO (TENO) scheme, known for its innovative weighting strategy, has demonstrated strong potential for complex flow predictions. This study extends the TENO weighting approach to develop non-oscillatory central TENO…

The compact finite difference method is a powerful tool for discretizing conservation laws, owing to its inherent flexibility in developing high-resolution and highly stable schemes. In this paper, we propose a framework for the design of…

This paper develops the high-order entropy stable (ES) finite difference schemes for multi-dimensional compressible Euler equations with the van der Waals equation of state (EOS) on adaptive moving meshes. Semi-discrete schemes are first…

Typical fully conservative discretizations of the Euler compressible single or multi-component fluid equations governed by a real-fluid equation of state exhibit spurious pressure oscillations due to the nonlinearity of the thermodynamic…

Multispecies kinematic flow models are defined by systems of N strongly coupled, nonlinear first-order conservation laws, where the solution is a vector of N partial volume fractions or densities. These models arise in various applications…

In this paper we present a class of high order accurate cell-centered Arbitrary-Eulerian-Lagrangian (ALE) one-step ADER-WENO finite volume schemes for the solution of nonlinear hyperbolic conservation laws on two-dimensional unstructured…

The modified dimension-by-dimension finite volume (FV) WENO method on Cartesian grids proposed by Buchm\"{u}ller and Helzel can retain the full order of accuracy of the one-dimensional WENO reconstruction and requires only one flux…

In this paper, a robustness-enhanced reconstruction for the high-order finite volume scheme is constructed on the 2-D structured mesh, and both the high-order gas-kinetic scheme(GKS) and the Lax-Friedrichs(L-F) flux solver are considered to…

This paper extends a new class of positivity-preserving, entropy stable spectral collocation schemes developed for the one-dimensional compressible Navier-Stokes equations in [1,2] to three spatial dimensions. The new high-order schemes are…

Due to its excellent shock-capturing capability and high resolution, the WENO scheme family has been widely used in varieties of compressive flow simulation. However, for problems containing strong shocks and contact discontinuities, such…

We propose a class of essentially non-oscillatory schemes with adaptive order (ENO-AO) for solving hyperbolic conservation laws. The new schemes select candidate stencils by novel smoothness indicators which are the measurements of the…

Centered numerical fluxes can be constructed for compressible Euler equations which preserve kinetic energy in the semi-discrete finite volume scheme. The essential feature is that the momentum flux should be of the form $f^m_\jph =…

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 develops high-order accurate, well-balanced (WB), and positivity-preserving (PP) finite volume schemes for shallow water equations on adaptive moving structured meshes. The mesh movement poses new challenges in maintaining the WB…

Active galactic nuclei, x-ray binaries, pulsars, and gamma-ray bursts are all believed to be powered by compact objects surrounded by relativistic plasma flows driving phenomena such as accretion, winds, and jets. These flows are often…

We propose a positivity preserving entropy decreasing finite volume scheme for nonlinear nonlocal equations with a gradient flow structure. These properties allow for accurate computations of stationary states and long-time asymptotics…