Convergence of a Fully Conservative Volume Corrected Characteristic Method for Transport Problems

We consider the convergence of a volume corrected characteristics-mixed method (VCCMM) for advection-diffusion systems. It is known that, without volume correction, the method is first order convergent, provided there is a nondegenerate diffusion term. We consider the advective part of the system and give some properties of the weak solution. With these properties we prove that the volume corrected method, with no diffusion term, gives a lower order L1-convergence rate of O(h/ t + h + (t)r), where r is related to the accuracy of the characteristic tracing. This result compares favorably to Godunov's method, but avoids the CFL constraint, so large time steps can be taken in practice. In fact, Godunov's method converges at O(h1/2), which is our result for t = Ch, where now C is not limited. However, the optimal choice, t = Ch2/(2r+1), gives a better

• Type: Journal
• Year: 2010
• Where: SIAMNUM
• Authors: Todd Arbogast, Wen-Hao Wang
• Keywords: Diffusion Term, Lower Order L1-convergence, Nondegenerate Diffusion Term, SIAMNUM 2010