We construct a local Lax-Friedrichs type positivity-preserving flux for compressible Navier-Stokes equations, which can be easily extended to high dimensions for generic forms of equations of state, shear stress tensor and heat flux. With this positivity-preserving flux, any finite volume type schemes including discontinuous Galerkin (DG) schemes with strong stability preserving Runge-Kutta tim...

This paper is devoted to the numerical approximation of the compressible Navier–Stokes equations with several independent entropies. Various models for complex compressible materials typically enter the proposed framework. The striking novelty over the usual Navier–Stokes equations stems from the generic impossibility of recasting equivalently the present system in full conservation form. Class...

The present paper deals with the continuous work of extending multi-dimensional limiting process (MLP) for higher-order discontinuous Galerkin (DG) methods to compute compressible Navier-Stokes equation. From the previous works, it was observed that the MLP shows several superior characteristics, such as efficient controlling of multi-dimensional oscillations and accurate capturing of complex f...

In this paper we develop a numerical method to solve Boltzmann like equations of kinetic theory which is able to capture the compressible Navier-Stokes dynamics at small Knudsen numbers. Our approach is based on the micro/macro decomposition technique, which applies to general collision operators. This decomposition is performed in all the phase space and leads to an equivalent formulation of t...

The governing equations for large-eddy simulation (LES) are derived from the application of a low-pass filter to the Navier-Stokes equations. It is often assumed that discrete operations performed on a particular grid act as an implicit filter, causing simulation results to be sensitive to the mesh resolution. Alternatively, explicit filtering separates the filtering operations from discretizat...

Introduction We describe recent developments in the design and implementation of nite element methods for the Navier-Stokes equations modelling chemically reactive ows. The emphasize is on the low-Mach number regime including the limit case of incompressible ow. The most important ingredients are residual driven a posteriori mesh reenement, fully coupled defect-correction iteration for lineariz...

We propose a two-population lattice Boltzmann model on standard lattices for the simulation of compressible flows. The is fully on-lattice and uses single relaxation time Bhatnagar–Gross–Krook kinetic equations along with appropriate correction terms to recover Navier–Stokes–Fourier equations. accuracy performance are analyzed through simulations benchmark cases including Sod shock tube, sound ...