The diffuse interface models, part of the family of the front capturing methods, provide an
efficient and robust framework for the simulation of multi-species flows. They allow the …

With progress on both the theoretical and the computational fronts, the use of Hermite
interpolation for mathematical modeling has become an established tool in applied science …

A reconstructed discontinuous Galerkin (RDG) method based on a hierarchical WENO
reconstruction, termed HWENO (P1P2) in this paper, designed not only to enhance the …

This work extends the flux-corrected transport (FCT) methodology to arbitrary order
continuous finite element discretizations of scalar conservation laws on simplex meshes …

We present a new perspective on the use of weighted essentially nonoscillatory (WENO)
reconstructions in high-order methods for scalar hyperbolic conservation laws. The main …

In this paper, a class of compact higher-order gas-kinetic schemes (GKS) with spectral-like
resolution will be presented. Based on the high-order gas evolution model, both the flux …

Abstract A Direct Discontinuous Galerkin (DDG) method is developed for solving the
compressible Navier–Stokes equations on arbitrary grids in the framework of DG methods …

A reconstructed discontinuous Galerkin (rDG (P1P2)) method, originally introduced for the
compressible Euler equations, is developed for the solution of the compressible Navier …

In this paper, we present a collection of algorithmic tools for constraining high-order
discontinuous Galerkin (DG) approximations to hyperbolic conservation laws. We begin with …

In the field of computational fluid dynamics, stability and convergence problems are often
encountered when solving the governing equation. This paper studies the effect of the mode …