Wave or Physics-Appropriate Multidimensional Upwinding Approach for Compressible Multiphase Flows

Abstract: This paper introduces multidimensional algorithms for simulating multiphase flows, leveraging the wave structure of the Euler equations in characteristic space and the physical properties of variables in physical space. The algorithm applies different reconstruction schemes to acoustic, vorticity, and entropy waves in characteristic space to enhance accuracy and minimize numerical artifacts. In characteristic space, upwind schemes are used for acoustic waves, central schemes for vorticity and entropy waves, and Tangent of Hyper-bola for INterface Capturing (THINC) reconstruction for material interfaces and contact discontinuities (a subset of entropy waves). This approach prevents spurious vortices in periodic shear layers, accurately captures vortical structures in gas-gas and gas-liquid interactions, and improves the accuracy of shock-entropy wave interactions. In physical space, phasic densities are computed using THINC in regions of contact discontinuities and material interfaces, while tangential velocities are calculated with central schemes to improve vortical structures. An adaptive reconstruction technique is also introduced to mitigate oscillations near shocks, which arise from primitive variable reconstruction, by combining primitive and characteristic variable reconstructions with the liquid phase being identified using the stiffened gas parameter. The proposed multidimensional upwinding approach outperforms traditional schemes, demonstrating superior accuracy in capturing physical phenomena, reducing numerical artifacts, and better matching experimental results across complex test cases.