A method for increased accuracy in Eulerian fluid dynamics calculations is described. The essence of the method is local cancellation of low-order, diffusional truncation errors. These errors are the source of nonlinear numerical instabilities. The methodology is described in general and specific application is made to the transient, two-dimensional flow equations for chemically reacting mixtures. Two example problems are solved to illustrate the method. For comparison, the same problems are solved with an artificial viscosity technique. (auth)