A Compact Local One-Dimensional Scheme for Solving a 3D N-Carrier System with Neumann Boundary Conditions

作者：Dai Weizhong^*

来源：Numerical Methods for Partial Differential Equations, 2010, 26(5): 1079-1098.

DOI：10.1002/num.20476

• 3D N-carrier system
• compact LOD finite scheme
• matrix analysis
• Neumann boundary condition
• stability

We consider a mathematical model for thermal analysis in a 3D N-carrier system with Neumann boundary conditions, which extends the concept of the well-known parabolic two-step model for micro heat transfer. To solve numerically the complex system, we first reduce 3D equations in the model to a succession of ID equations by using the local one-dimensional (LOD) method. The obtained ID equations are then solved using a fourth-order compact finite difference scheme for the interior points and a second-order combined compact finite difference scheme for the points next to the boundary, so that the Neumann boundary condition can be applied directly without discretizing. By using matrix analysis, the compact LOD scheme is shown to be unconditionally stable. The accuracy of the solution is tested using two numerical examples. Results show that the solutions obtained by the compact LOD finite difference scheme are more accurate than those obtained by a Crank-Nicholson LOD scheme, and the convergence rate with respect to spatial variables is about 2.6.

• 出版日期2010-9