High Resolution Numerical Methods And Adaptive Mesh Refinement Algorithms For Compressible Multi-Fluid Dynamics

This thesis presents the high resolution numerical simulation methods for multi-fluid dynamics. The main contents include three parts: The first is a set of interface capturing equations deduced to describe the interface evolution, which is suitable for constructing two-order enhanced un-split finite volume scheme and three-order Parabolic-Piecewise-Method (PPM) scheme in Euler coordinate; The second is the capabilities of Level-Set method for tracking multi-fluid interfaces are unproved; The third is that the computational resolutions are much more advanced by improving Adaptive Mesh Refinement (AMR) technique.Interface capturing method for multi-fluid flow, which smear out the tangential discontinuity, is developed to simulate the compressible flow. The multi-fluid problems can be transformed to a single-fluid to resolve, using the fluid dynamic conservative equations coupled with the interfaces capturing equations, and any of stability and non-oscillation scheme for the whole computational region. The two schemes mentioned above are better. Level set method and AMR technique are assistant instruments for improving the capabilities of the codes and advancing the accuracy of the solutions.Range application of the interface capturing method and its efficient equations by Shyue confined within Mie-Grtlneisen equation of state (EOS) are extended in form ofand verified in polynomial EOS.Two-order enhanced un-split finite volume Euler method for multi-fluid flow, which combines the Roe approximate Riemann solver, is developed to simulate the multi-fluid interactions, such as the fluid described by polynomial EOS, Stiffen gas EOS , Jones-Wilkins-Lee(JWL) gaseous explosive EOS, Cochran-Chan(CC) solid explosive EOS and HOM shock wave EOS, etc. Numerical results of the ID, 2D and 3D multi-fluid interaction examples show that the high-resolution method and interface capturing equations can resolve the multi-fluid flow correctly and successfully.A simple fluid-mixture type PPM algorithm for multi-fluid flow, which is based on VOF interface capturing method and resolved by Langange/Remap two steps, is developed to simulate the high density or high pressure ratio flow at both sides of the interface. This is the first time to utilize the method to simulate two-dimensional impedance gradient flier quasi-isentropic compression and launch the flier to hypervelocity in our country. Numerical results are consistent with that of Sandia laboratory experiment and agree with that of CTHcode too.An adaptive mesh refinement under 2D Euler structure grid for multi-fluid flow is developed for resolving Richtmyer-Meshkov, Rayleigh-Taylor and Helmholtz multi-fluid instabilities, and the high resolution interface properties can be obtained. In addition, we compared the CPU time for a model with 3 levels AMR grid and the same accuracy uniform grid. It's about 8 times for the latter over the former. We also used 5 levels AMR grid to simulate the Helmholtz multi-fluid instability, but not compared the CPU time with each other yet.Based on the interface capturing methods, the fluid dynamic programs have capabilities of dealing with the complex interfaces, unforeseeing topology changes, and extending easily to simulate 3D problems.