Large time step HLL and HLLC schemes

Asymptotic Preserving Hll Schemes

This work concerns the derivation of HLL schemes to approximate the solutions of systems of conservation laws supplemented by source terms. Such a system contains many models such as the Euler equations with high friction or the M1 model for radiative transfer. The main difficulty arising from these models comes from a particular asymptotic behavior. Indeed, in the limit of some suitable parame...

High-Resolution Large Time-Step Schemes for Hyperbolic Conservation Laws

Large Time Step and Asymptotic Preserving Numerical Schemes for the Gas Dynamics Equations with Source Terms

We propose a large time step and asymptotic preserving scheme for the gas dynamics equations with external forces and friction terms. By asymptotic preserving, we mean that the numerical scheme is able to reproduce at the discrete level the parabolic-type asymptotic behaviour satisfied by the continuous equations. By large time-step, we mean that the scheme is stable under a CFL stability condi...

Thermodynamics and kinetics of large-time-step molecular dynamics

Molecular dynamics (MD) simulations provide essential information about the thermodynamics and kinetics of proteins. Technological advances in both hardware and algorithms have seen this method accessing timescales that used to be unreachable only few years ago. The quest to simulate slow, biologically relevant macromolecular conformational changes, is still open. Here, we present an approximat...

A HLL nc (HLL nonconservative) method for the one-dimensional nonconservative Euler system

An adaption of the original HLL scheme for the one-dimensional nonconservative Euler system modeling gaz flow in variational porosity media is proposed . Numerical scheme is detailed and algorithm is tested with two Riemann problems.