| Summary: | 博士 === 國立臺灣大學 === 土木工程學研究所 === 93 === The Eulerian-Lagrangian method of fundamental solutions (ELMFS), which is a combination of the method of fundamental solutions (MFS) and the Eulerian-Lagrangian method (ELM), is proposed in this thesis to deal with the advection-diffusion, Burgers’ and Navier-Stokes equations. The ELM is adopted to convert the non-linear partial differential equations including the convective terms to the linear time-dependent partial differential equations and then the resultant partial differential equations are solved by the MFS based on the time-dependent fundamental solution.
Initially, the proposed ELMFS is used to analyze 1D, 2D and 3D advection-diffusion equations which describe transport phenomena. The results of advection-diffusion equations are almost identical with the analytical solutions and other numerical results. Then the ELMFS is adopted to study the solutions of the multi-dimensional Burgers’ equations. During the solution procedures, the unknowns in the partial differential equations are decoupled in order to improve the efficiency of the simulation. Furthermore, the time-dependent MFS and the unsteady Stokeslets are combined together to solve the unsteady Stokes problems. The flexibility and the robustness of the MFS are demonstrated by solving the unsteady Stokes problems in irregular domains as well. Finally, the ELMFS based on the unsteady Stokeslets is adopted to analyze the Navier-Stokes equations in primitive-variable form. The stability and the consistency of the proposed ELMFS are examined in a series of numerical experiments, which demonstrate that the ELMFS can be considered as a simple and efficient numerical method in handling the nonlinear partial differential equations with convective terms.
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