Numerical Simulation Of Flow Around Submerged Body And Coupled Bay-river System

This paper is to investigate the numerical simulation of two partial differential equation boundary value problems on unbounded domains, which arc derived from fluid dynamics. One essential difficulty of the given problems for computation is the unboundcdncss of the physical domains. We use the artificial boundary condition method to overcome this difficulty. Namely for the given problem we introduce some suitable artificial boundaries to divide the unbounded physical domain into the bounded computational domain and unbounded part and set up high order artificial boundary conditions on the given artificial boundaries. Then we can reduce the original problem to a boundary value problem defined on the bounded computational domain. Furthermore, we can get the equivalent variational form for the reduced boundary value problem. Finally we use the finite clement method to get an approximate solution. The numerical solution would be a good approximation of the original solution restricted in the computational domain.Calculation of the potential flow around a submerged body is an important problem in applications. The problem is defined on an unbounded physical domain. We apply the artificial boundary condition method to solve it. We study the test function space carefully, then make the correct choice of test functions, such that test function space matches with the solution function space in each problem. For 2D case, we design high order global and local artificial boundary conditions. For 3D case, the computational cost increases and the design of artificial boundary conditions becomes more difficult, we successfully design high order global artificial boundary condition.Calculating the complex amplitude in a coupled bay-river system is another fluid dynamics problem coming from engineering application. This is also a problem defined on an unbounded physical domain. Due to the property of the solution of this problem, we introduce a semi-circular artificial boundary in the unbounded physical domain and design high order artificial boundary conditions on it.In each chapter, some numerical examples arc given to show the practicabilityand effectiveness of the given artificial boundary condition method.