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SIAM J. NUMER. ANAL. c 2010 Society for Industrial and Applied Mathematics Vol. 48, No. 3, pp. 797823
 

Summary: SIAM J. NUMER. ANAL. c 2010 Society for Industrial and Applied Mathematics
Vol. 48, No. 3, pp. 797823
CONVERGENCE OF A FULLY CONSERVATIVE
VOLUME CORRECTED CHARACTERISTIC METHOD
FOR TRANSPORT PROBLEMS
TODD ARBOGAST AND WEN-HAO WANG
Abstract. 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
rate, O(h2r/(2r+1)), than Godunov's method, e.g., O(h2/3) if r = 1. With a nondegenerate diffusion
term, we obtain an L2-error estimate for the problem. We also prove the existence of, and give an
error estimate for, a perturbed velocity field for which the volume is locally conserved. Finally, some

  

Source: Arbogast, Todd - Center for Subsurface Modeling & Department of Mathematics, University of Texas at Austin

 

Collections: Mathematics; Geosciences