In these proceedings we are interested in quantitative estimates for advective equations with an anelastic constraint in presence of vacuum. More precisely, we derive a quantitative stability estimate and obtain the existence of renormalized solutions. Our main objective is to show the flexibility of the method introduced recently by the authors for the compressible Navier-Stokes’ system. This ...

Lattice Boltzmann equations (LBE) are a useful tool for simulating the incompressible Navier-Stokes equations. However, LBE actually simulate a compressible but usually isothermal fluid at some small but finite Mach number. There has been recent interest in using LBE at larger, but still subsonic, Mach numbers, for which the viscous terms in the resulting momentum equation depart appreciably fr...

We present directional operator splitting schemes for the numerical solution of a fourth-order, nonlinear partial differential evolution equation which arises in image processing. This equation constitutes the H−1-gradient flow of the total variation and represents a prototype of higher-order equations of similar type which are popular in imaging for denoising, deblurring and inpainting problem...

The Multiscale Finite-Volume (MSFV) method has been recently developed and tested for multiphase-flow problems with simplified physics (i.e. incompressible flow without gravity and capillary effects) and proved robust, accurate and efficient. However, applications to practical problems necessitate extensions that enable the method to deal with more complex processes. In this paper we present a ...

Climate warming over the next century is expected to have a large impact on the interactions between pathogens and their animal and human hosts. Vector-borne diseases are particularly sensitive to warming because temperature changes can alter vector development rates, shift their geographical distribution and alter transmission dynamics. For this reason, African trypanosomiasis (sleeping sickne...

This paper discusses numerical and modeling issues that arise in cell-centered finitevolume methods (FVM) for large eddy simulation (LES) of compressible flows on unstructured grids. These are: accuracy and stability of flux interpolation scheme, shock capturing strategy, and subgrid-scale (SGS) modeling. To enhance the accuracy of flux reconstruction, a new scheme with added first derivative t...

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...

A vertex-based finite volume method for Laplace operator on triangular grids is proposed in which Dirichlet boundary conditions are implemented weakly. The scheme satisfies a summation-by-parts (SBP) property including boundary conditions which can be used to prove energy stability of the scheme for the heat equation. A Nitsche-type penalty term is proposed which gives improved accuracy. The sc...