Very simple linearisations for the solution to the Riemann problem for the
time-dependent and for the steady supersonic Euler equations are presented.
When used locally in conjunction with Godunov-type methods, computing ...
The time-dependent Euler equations of Gas Dynamics are a set of non-linear hyperbolic conservation laws that admit discontinuous solutions (e.g. shocks). In this paper we are concerned with Riemann-problem based numerical ...
We explore how the Weighted Average Flux (WAF) approach can be used to generate first and second order accurate finite volume schemes in one, two and three space dimensions. The derived schemes have multidimensional upwinding ...
The Artificial Compressibility approach is an important numerical method for solving the incompressible Navier-Stokes Equations. The application of high resolution numerical methods to the equations of the artificial ...
The solution to the Incompressible Navier-Stokes equations still represents a significant numerical challenge. The reason for this is that there is a lack of coupling between velocity and pressure. This means that the ...
Three topics on modern shock capturing methods for the time-dependent Euler equations of Gas Dynamics are addressed. First we present the Weighted Average Flux Method (or WAF), one of several Riemann-problem based shock ...
We present Numerical Viscosity Functions, or NVFs, for use with Riemann-problem based shock-capturing methods as applied to viscous flows. In particular, viscous flux limiters are derived. The analysis pertain to a linear ...