Accuracy of Difference Formulation of Navier-Stokes Equations

An error analysis is formulated under the assumption that Lax's equivalence theorem is valid for quasilinear equations. Analysis is carried out for a class of difference approximations of the Burgers' equation. Explicit estimates of the errors due to various sources are obtained and verified by numerical integration. The boundary errors do not decay rapidly away from the boundary and often dominate the truncation errors. The boundary errors led to significant differences between apparently smooth and physically reasonable results of carefully executed computations of the same problem. The results based on difference formulations that are more nearly consistent with the differential formulation are likely to be more accurate. A conservative difference formulation is proposed to meet this consistency requirement as far as is practically possible. Calculations of multidimensional flow examples guided by these inferences are given. The results tend to support such inferences.