A Linearised Riemann Solver for Godunov-Type Methods

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 savings by a factor of about four, relative to the use of exact Riemann solvers, can be achieved. For severe flow regimes...

Viscous Flux Limiters

Paper presented at the 9th GAMM Conference on Numerical Methods of Fluid Mechanics, Laussane, Switzerland, September 1991. 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...

Some aspects of shock capturing methods for gas dynamics

Three topics on modern shock capturing methods for the time-dependent Euler equations of Gas Djméimics are addressed. First we present the Weighted Average Flux Method (or WAF), one of several Riemêinn-problem based shock capturing methods. Then we deal with the Riemann problem. We present an efficient exact Riemann solver, a robust non...

A linearised Reimann solver for the time-dependent Euler equations of gas dynamics

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 methods for solving the general initial-value problem for these equations. We present an approximate, lineeu'ised Riemann...

Numerical Computation of Two-Dimensional Unsteady Detonation Waves in High Energy Solids

We are concerned with theoretical modelling of unsteady, two-dimensional detonation waves in high energy solids. A mathematical model and a numerical method to solve the associated hyperbolic system of equations are presented. The model consists of the Euler equations augmented bby extra conservation laws and source terms to accoxint for...

Riemann Problems and the WAF Method for the Two-Dimensional Shallow Water Equations

An exact Riemann solver for the shallow water equations along with several approximate Riemann solvers are presented. These solutions are used locally to compute numerically the global solution of the general initial boundary value problem for the shallow water equations. The numerical method used is the weighted average flux method (WAF)...

The Dry-Bed Problem in Shallow-Water Flows

Starting in 1946 as the College of Aeronautics, the Cranfield Institute of Technology was granted university status in 1969. In 1993 it changed its name to Cranfield University.

TVD regions for the weighted average flux (WAF) method as applied to a model hyperbolic conservation law

Oscillation-free versions of the weighted average flux (WAF) method for the model equation ut aux = 0 are presented. Two approaches are discussed in detail namely. Courant Number amplification and flux, or weight, limiting. Extended TVD regions are derived and amplifying/limiting functions are constructed. Numerical experiments on and ul aux = 0...

A Fast Riemann Solver with Constant Covolume Applied to the Random Choice Method

The Riemann problem for the unsteady, one dimensional Euler equations together with the constant-covolume equation of state is solved exactly. The solution is then applied to the Random Choice Method to solve the general initialboundary value problem for the Euler equations. The iterative procedure to find p*, the pressure between the acoustic...

The Random Choice Method on a non-staggered grid utilising an efficient Riemann solver

A practical description of the Random Choice Method (RCM) on non-staggered grids is presented. The original idea appears to be due to Colella (1982). The approach is much simpler than the staggered grid version of RCM, which is the one traditionally used. It also offers a number of advantages with regards to use of non-regular meshes in space...

Numerical studies of a detonation analogue

Starting in 1946 as the College of Aeronautics, the Cranfield Institute of Technology was granted university status in 1969. In 1993 it changed its name to Cranfield University.

A New Numerical Technique for Quasi-Linear Hyperbolic Systems of Conservation Laws

A new computational method for hyperbolic conservation laws in one space dimension is presented. This technique is based on the Random Choice Method (RCM). The first step is exactly as in RCM with secondary grid, whereby intercell values at half time levels are provided. The second step completes the solution at time level n 1 via a finite...

Mesh effects on the computation of non-linear gravity waves of arbitrary discharge

Numerical computations of non-linear gravity uaues are presented and the effects of mesh variations on the results are discussed. Waves are regarded as tujo-parameter families (X,A) of arbitrary discharge Q, and computations are carried out using a new Kantorovich algorithm. Mesh effects are to a large extent, dependent on the particular uiave...

Transition Bifurcation Branches in Non- Linear Water Waves

Starting in 1946 as the College of Aeronautics, the Cranfield Institute of Technology was granted university status in 1969. In 1993 it changed its name to Cranfield University.