A weak formulation of Roe's approximate Riemann Solver applied to 'Barotropic' flows

A weak formulation of Roe's approximate Riemann solver is applied to the equations of ‘barotropic’ flow, including the shallow water equations, and it is shown that this leads to an approximate Riemann solver recently presented for such flows.

A Riemann solver for compressible flow of a real gas in a Lagrangian frame

An approximate Riemann solver is presented for the compressible flow equations with a general (convex) equation of state in a Lagrangian frame of reference.

An efficient Riemann solver for unsteady flows with non-ideal gases

A Riemann solver is presented for the Euler equations of gas dynamics with real gases. This represents a more efficient version of an algorithm originally presented by the author.

Efficient shock capturing for isentropic flows using arithmetic averaging

A shock capturing scheme is presented for the equations of isentropic flow based on upwind differencing applied to a locally linearized set of Riemann problems. This includes the two-dimensional shallow water equations using the familiar gas dynamics analogy. An average of the flow variables across the interface between cells is required, and this average is chosen to be the arithmetic mean for computational efficiency, leading to arithmetic averaging. This is in contrast to usual ‘square root’ averages found in this type of Riemann solver where the computational expense can be prohibitive. The scheme is applied to a two-dimensional dam-break problem and the approximate solution compares well with those given by other authors.