| Summary: | 碩士 === 國立臺灣海洋大學 === 河海工程學系 === 100 === In this thesis, the local RBF collocation method (LRBFCM) is proposed to analyze the double-diffusive natural convection in porous media with steady, unsteady and anisotropic material. The double-diffusive natural convection in porous media is one kind of diffusive phenomenon caused by temperature and concentration gradients. This physical problem has been investigated for decades because it covers many fields of engineering, such as nuclear reactors, ground water pollution and geophysical systems, etc. Although there have been many successful studies to analyze this issue, in viewpoint of its importance, it is still worth to be investigated by other potential numerical methods.
LRBFCM is adopted for spatial discretization. It is a promisingly meshless method which does not need mesh generation, numerical integration, and can overcome the disadvantages of full matrix and ill-conditioned system. For unsteady problem, the implicit Euler method (IEM) is a stable scheme and used for discretization for real time axis. A system of nonlinear algebraic equations (NAEs) will be formed, after LRBFCM and IEM to discretize partial differential equations (PDEs). Then, exponentially convergent scalar homotopy algorithm (ECSHA) is adopted to solve the system of NAEs. It is a newly-developed solver which has exponentially convergent rate and is free from calculation of inverse Jacobian matrix. Hence, it only costs few computational resources in every iterated step.
There are some numerical examples presented in this thesis to verify the feasibility and accuracy of the proposed meshless numerical methods. For stability test, the results by using different numerical parameters are also displayed and compared with other solutions.
|
|---|
