Computational Accuracy and Mesh Reynolds Number
Abstract
The steadystate Burgers' equation uu_{x} = (I /Re) u _{xx} (0 ⩽ x ⩽ 1) with boundary values u(0) = 0 and u(1) = 1 is employed as a model equation for fluid dynamics. It is shown how different conservative discretizations of the nonlinear term uu _{x} govern the discretization error in computational results, especially when the mesh Reynolds number Re Ax is not small. For a particular choice of the nonlinear discretization, the maximum error in the computed result can attain a value at some fairly large Red x comparable to that expected at a much smaller ReΔ x. The formal order of accuracy of an algorithm, in terms of either Δ x or ReΔ x, does not reflect the accuracy of computational results, especially when the mesh is coarse.
 Publication:

Journal of Computational Physics
 Pub Date:
 September 1978
 DOI:
 10.1016/00219991(78)900566
 Bibcode:
 1978JCoPh..28..315C