Flux Splitting for Stiff Equations: A Notion on Stability

Flux Splitting for Stiff Equations: A Notion on Stability

For low Mach number flows, there is a strong recent interest in the development and analysis of IMEX (implicit/explicit) schemes, which rely on a splitting of the convective flux into stiff and nonstiff parts. A key ingredient of the analysis is the so-called Asymptotic Preserving (AP) property, which guarantees uniform consistency and stability as the Mach number goes to zero. While many autho...

Flux Splitting: A Notion on Stability

In the context of low Mach number flows, successful methods are Asymptotic Preserving and IMEX schemes. Both schemes for hyperbolic equations rely on a splitting of the convective flux into stiff and nonstiff parts. This choice is not arbitrary and has an influence on both the stability and the accuracy of the resulting methods. In this work, we consider a first-order IMEX scheme based on diffe...

A Stability Notion for Lattice Boltzmann Equations

On Kinetic Flux Vector Splitting Schemes for Quantum Euler Equations∗

The kinetic flux vector splitting (KFVS) scheme, when used for quantum Euler equations, as was done by Yang et al [22], requires the integration of the quantum Maxwellians (Bose-Einstein and Fermi-Dirac distributions), giving a numerical flux much more complicated than the classical counterpart. As a result, a nonlinear 2 by 2 system that connects the macroscopic quantities temperature and fuga...

A Modified Flux Vector Splitting Scheme for Flow Analysis in Shock Wave Laminar Boundary Layer Interactions

The present work introduces a modified scheme for the solution of compressible 2-D full Navier-Stokes equations, using Flux Vector Splitting method. As a result of this modification, numerical diffusion is reduced. The computer code which is developed based on this algorithm can be used easily and accurately to analyze complex flow fields with discontinuity in properties, in cases such as shock...