Heat Conduction Simulation of 2D Moving Heat Source Problems Using a Moving Mesh Method

Algorithm 1.

Flowchart of the moving mesh algorithm for moving heat source problem.

Input: The end time , initial physical mesh (, ) and initial temperature field .

Output: The final physical mesh (, ) and the corresponding temperature field .

1 Let and ;

2 while do

3  Determine the time step ;

4  Compute the 1D monitor functions on for all , and on for all , based on the current physical mesh (, ) and the corresponding temperature field ;

5  Solve two linear systems of discretization of 1D MMPDE6 with and , respectively, to get two new 1D mesh and ;

6  Construct the new physical mesh (, );

7  Solve the system of discretization (12) to get the new temperature field ;

8  Let and ;

9 end