Extension of the hybrid WENO5IS-THINC scheme to compressible multiphase flows with an arbitrary number of components

Abstract

We extend the hybrid reconstruction method combining the fifth-order incremental-stencil weighted essential non-oscillatory (WENO5IS) with the Tangent of Hyperbola for INterface Capturing (THINC) to flow scenarios involving an arbitrary number of fluids. The extended five-equation model accounting for both capillary and viscous forces is employed, maintaining permutation symmetry among fluid components. Within the finite volume (FV) framework employing structured meshes, the WENO5IS scheme, augmented with a positivity-preserving limiter accurately resolves flow structures inside each component, while the symmetry-preserving THINC sharpens the fluid interfaces. Interface regions containing multiple components are decomposed into pairs of interfaces between each involved component, and the corresponding reconstructed volume fractions and phase densities are renormalized before time integration. The inclusion of a generalized continuous surface force (CSF) method enables simulation of capillary effects between an arbitrary number of fluids. One- and two-dimensional test cases involving multiple components are employed to validate the efficacy of the proposed approach in maintaining interface sharpness, achieving high-resolution within individual components, and preserving normalization and positivity properties of volume fractions. Simulations incorporating surface tension and viscosity further demonstrate the applicability of the present model and algorithm in capillary problems within the compressible framework.