4 papers
On the Spectral Properties of Van Leer and AUSM Flux-Vector Splitting Schemes
Zhengrong Xie, Zheng Li
The flux-vector splitting scheme of Van Leer is a cornerstone of computational fluid dynamics, yet its original proof of the eigenvalue sign condition was presented in a condensed…
Numerical Analysis and Dimension Splitting for A Semi-Lagrangian Discontinuous Finite Element Scheme Based on the Characteristic Galerkin Method
Zhengrong Xie
A semi-Lagrangian discontinuous finite element scheme based on the characteristic Galerkin method (CSLDG) is investigated, which directly discretizes an integral invariant model de…
Well-posedness and Regularity of the Integral Invariant Model from Linear Scalar Transport Equation
Zhengrong Xie
An integral invariant model derived from the coupling of the transport equation and its adjoint equation is investigated.Despite extensive research on the numerical implementation…
Runge-Kutta Discontinuous Galerkin Method Based on Flux Vector Splitting with Constrained Optimization-based TVB(D)-minmod Limiter for Solving Hyperbolic Conservation Laws
Zhengrong Xie
The flux vector splitting (FVS) method has firstly been incorporated into the discontinuous Galerkin (DG) framework for reconstructing the numerical fluxes required for the spatial…