An approximate linearized characteristic Riemann solver based on blending of Riemann invariants

A new linearized characteristic upwind approximate Riemann solver is proposed based on the blending of the Riemann invariants. The scheme is based on the linearization of the differential relations along the characteristic curves of the one-dimensional hyperbolic conservation laws. It involves construction of the parameters at the cell interface such that they are consistent with the system of characteristic relations. A third order MUSCL reconstruction was used in the present work. Upwinding in the scheme is carried out by upwinding of the Riemann invariants. In this paper the development of the scheme from the compatibility relations for the Euler equations is described. The scheme was then applied to solve various cases of shock tube problems, two-dimensional Riemann problems and finally, as a practical example, it was used to carry out LES of a subsonic jet. The scheme was found to perform remarkably well for all the cases and is extremely computationally efficient, thus making it ideal for practical applications where high accuracy and high speed computation are required.