Well-balanced schemes versus fractional step method for hyperbolic systems with source terms

Abstract

The paper is devoted to the analysis of the true accuracy of different schemes when computing a simple hyperbolic model with source terms, which describes the motion of two-phase flows including source terms. The strategy of upwinding the source terms is investigated and compared with the standard fractional step method. A first scheme relies on the usual fractional step approach. A second scheme applies for upwinding of source terms. It, however, does not provide satisfactory results when computing certain specific unsteady cases. This behaviour can be easily explained. It thus motivates us to introduce a third scheme, which is similar to the previous but aims at providing an increased accuracy on coarse meshes when computing highly unsteady flows. This latter scheme requires us to define a cell scheme which computes the void fraction with the help of a modified governing equation, while using the same interface solver. A detailed numerical study which includes a measure of the L 1 norm of the error completes the work.