Gridless Method For The Simulation Of Heat Conduction

The main purpose of this thesis is to develop a gridless method of the solution of heat conduction which called FPM. FPM was used widely in the area of CFD. The works presented in the thesis are as follows:Firstly, in the discretization of computational region, the points are generated by the structural method. Clouds with points are built on the base of a number of discrete grid nodes. Double structure clouds with points and local least-squares curve fits are applied to obtain the second spatial derivatives, which is different from the traditional gridless method. Then dummy nodes are added to deal with the boundary condition, parameters of the dummy nodes lie on the type of the boundary condition. At last, an explicit multistage Runge-Kutta algorithm is used to advance the discrete conduct equations, without considering the equation steady or not.For the sake of demonstrating the accuracy and applicability of the gridless method discussed in this thesis, a number of examples with different boundary conditions are computed respectively, and the results are satisfying. In the end of the thesis, some parameters in the gridless method, which influence the precision, such as the radii of clouds, are also discussed in the numerical simulation.