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 …

Many mathematical models of continuum mechanics are derived from integral conservation
laws. Examples of such models include the Euler and Navier–Stokes equations of fluid …

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 …

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 …

In this paper, we construct a positivity-preserving high order accurate finite volume hybrid
Hermite Weighted Essentially Non-oscillatory (HWENO) scheme for compressible Navier …

In this work, we present HODG, an open-source component-based development framework
based on high order Discontinuous Galerkin (DG) methods for solving compressible Euler …