High-Resolution Numerical Methods for Compressible Multi-Fluid Flows and their Applications in Simulations

Abstract

This thesis is concerned with the development of high-resolution diffuse interface methods for resolving compressible multi-fluid flows and their applications in simulations. An inviscid compressible multi-fluid model is recovered. The viscous effect and gravity can also be introduced. The direct Eulerian piecewise parabolic method (PPM) is generalized to integrate numerically the hyperbolic part of governing equations. Adaptive mesh refinement (AMR) is built into hydrodynamic code. MUSCL-Hancock method and PPM are extended to resolve the multi-fluid flows with components modeled by Mie-Grüneisen equation of state (EOS). Methods based on Lagrangian-remapping (LR) PPM are developed to simulate flows involving one or two barotropic components. LR PPM is applied to numerically study RMI driven by a cylindrical shock. Random-mode perturbations are imposed on air-helium interface to mimic real problems. The study also concentrates on the numerical investigation of cylindrical and spherical bubbles in air accelerated by shock with Mach numbers (Ma) in the range of 1.2 &lt Ma &lt 6.