A fifth-order high-resolution shock-capturing scheme based on modified weighted essentially non-oscillatory method and boundary variation diminishing framework for compressible flows and compressible two-phase flows

On high-order accurate weighted essentially non-oscillatory and discontinuous Galerkin schemes for compressible turbulence simulations.

In this article, we give a brief overview on high-order accurate shock capturing schemes with the aim of applications in compressible turbulence simulations. The emphasis is on the basic methodology and recent algorithm developments for two classes of high-order methods: the weighted essentially non-oscillatory and discontinuous Galerkin methods.

High-resolution simulation of cavitation in compressible two-phase flows

The aim of this research project is to take an existing compressible two-phase flow solver and to turn it into a fully parallelized scalable MPI code capable of simulating three-dimensional geometries at unprecedented resolution with high fidelity to the basic physics. The existing code has been developed by several academics (Stephen Shaw, Xi’an JiaotongLiverpool University, and Peter Spelt, E...

Numerical viscosity and resolution of high-order weighted essentially nonoscillatory schemes for compressible flows with high Reynolds numbers.

A quantitative study is carried out in this paper to investigate the size of numerical viscosities and the resolution power of high-order weighted essentially nonoscillatory (WENO) schemes for solving one- and two-dimensional Navier-Stokes equations for compressible gas dynamics with high Reynolds numbers. A one-dimensional shock tube problem, a one-dimensional example with parameters motivated...

A high order moving boundary treatment for compressible inviscid flows

We develop a high order numerical boundary condition for compressible inviscid flows involving complex moving geometries. It is based on finite difference methods on fixed Cartesian meshes which pose a challenge that the moving boundaries intersect the grid lines in an arbitrary fashion. Our method is an extension of the so-called inverse Lax-Wendroff procedure proposed in [16] for conservation...

A Two -Step Modification toward Implementing Compressible Source Terms in Low Compressible Flows