A simplified approach for simulations of multidimensional compressible multicomponent flows: The grid-aligned ghost fluid method

Abstract

In the present work the authors present a simplified formulation for the extension of a ghost fluid method in multidimensional space. In the proposed method, the Riemann problems at the interface are formulated along the grid rather than in a normal to the interface direction. The information that is required to construct these Riemann problems is acquired “on-the-fly” from the adjacent to the interface cells. With respect to existing multidimensional ghost fluid formulations, the method is computationally less expensive, as the procedures of determining ghost fluid regions, extending, interpolating and extrapolating variables and computing geometrical quantities are avoided. More importantly, it is markedly simple with respect to its implementation. By introducing the proposed formulation in a well-established front tracking framework we perform an extensive validation of the method and demonstrate that despite its simplicity it yields highly accurate results while remaining free of oscillations.