Meshless Local Petrov-Galerkin Collocation Method for Two-dimensional Heat Conduction Problems

摘要

Meshless local Petrov-Galerkin collocation method is applied to compute two-dimensional heat conduction problems in irregular domain. By taking the Dirac's Delta function as the test function, the local domain integration is avoided. The essential boundary conditions can be implemented easily in this method. A case that has analytical solution shows the present method can obtain desired accuracy and efficient. Two cases in engineering are computed to validate the approach by comparing the present method with the finite volume method (FVM) solutions obtained from a commercial CFD package FLUENT 6.3. The results show that the present method is in good agreement with the FLUENT 6.3, and has very high computational precision. The proposed method, which is a truly meshless method, can describe the boundaries of irregular domain more accurately, and be very easy to be implemented in engineering.