Notes on the ExactPack Implementation of the DSD Rate Stick Solver

[摘要] It has been shown above that the discretization scheme implemented in the ExactPack solver for the DSD Rate Stick equation is consistent with the Rate Stick PDE. In addition, a stability analysis has provided a CFL condition for a stable time step. Together, consistency and stability imply convergence of the scheme, which is expected to be close to first-order in time and second-order in space. It is understood that the nonlinearity of the underlying PDE will affect this rate somewhat. In the solver I implemented in ExactPack, I used the one-sided boundary condition described above at the outer boundary. In addition, I used 80% of the time step calculated in the stability analysis above. By making these two changes, I was able to implement a solver that calculates the solution without any arbitrary limits placed on the values of the curvature at the boundary. Thus, the calculation is driven directly by the conditions at the boundary as formulated in the DSD theory. The chosen scheme is completely coherent and defensible from a mathematical standpoint.

[发布日期] 2016-08-01

[学科分类] 数学（综合）