High Precision Numerical Scheme Of Adaptive Method For Complex Multi-phase Flow

High precision numerical simulation is one of the hot research fields in com-putational fluid dynamics.The way of improving numerical precision includes but not limited to using high-order numerical scheme and adaptive mesh method which are used in this paper.There are three main parts as follows:high-order moving meshes scheme,the two-stage fourth order accurate temporal scheme of complex fluid,and adaptive multi-resolution method of reactive multi-phase flow of sharp interface scheme.In Chapter 2,a high-order moving meshes method based on modified Runge-Kutta method and WENO scheme is developed.This scheme is based on remapping-free Arbitrary-Lagrangian-Eulerian(ALE),which constructs the semi-discrete equation systems with finite volume method beginning from the integral form of Euler equation with arbitrary meshes speed.Considering that the mesh movement will lead to the mesh deformation in the local area,a stable third-order WENO reconstruction method is adopted to achieve the high-order spatial preci-sion.The traditional Runge-Kutta method is only suitable for fixed grid problem which can not be directly applied to moving meshes method.Therefore,a mod-ified Runge-Kutta method is adopted,which updates the cell size and grid node speed in each Runge-Kutta time step,so that it can be applied to high-order moving meshes scheme.The numerical results show that the scheme can not only achieve high order precision in the smooth problem,but also can track the shock wave well and guarantee the quality of the grid without causing the distortion and deformation of the mesh.In Chapter 3,a high order numerical scheme with complex fluid based on Lax-Wendroff solver is researched.A approximate method with stiffened gas EOS in local area is adapted,because the general equation of state(EOS)is so com-plex that exact Riemann solver can not be solved directly.This approximate method is based on the idea of iteration,and that the stiffened gas EOS is lo-cal approximate to general EOS is used in each iteration.These solutions are used to determine new states of the fluid at points on the original branches of the(u,p)-diagrams.The Riemann problem is again solved in the same manner as at the previous iterations with initial data corresponding to the newly found states.A recent two-stage fourth order accurate temporal discretization based on the Lax-Wendroff type solvers is adopted,which maintains not only the simplic-ity of Runge-Kutta method but also temporal-spatial coupled of Lax-Wendroff scheme.A cubic convergence rate inverse Hermite interpolation is use to ensure efficiency of iteration in Riemann problem.It can be seen from the numerical results that the method has high precision and robustness,and the test results of convergence order are given.In Chapter 4,adaptive multi-resolution method is applied to the stiffened gas EOS of reactive multi-phase flow problem.The sharp interface method is applied to maintain the conservation near the interface in this paper,and interface is track and deal with by level set method and ghost fluid method,which may handle the topological changes naturally and reduce the error near the interface.Also,high efficient storage pyramid data structure and adaptive multi-resolution method are used to improve the efficiency of the calculation of numerical simulation.The robustness and stability of the scheme are demonstrated by a large number of numerical examples,and the numerical results of the adaptive method and the non-adaptive method are compared to show the superiority of the adaptive method...