A posteriori pointwise error estimation for compressible fluid flows using adjoint parameters and Lagrange remainder

A.K. Alekseev, I. M. Navon

The pointwise error of a finite-difference calculation of supersonic flow is discussed. The local truncation error is determined by a Taylor series with the remainder being in a Lagrange form. The contribution of the local truncation error to the total pointwise approximation error is estimated via adjoint parameters. It is demonstrated by numerical tests that the results of the numerical calculation of gasdynamics parameter at an observation point may be refined and an error bound may be estimated. The results of numerical tests for the case of parabolized Navier-Stokes (PNS) are presented as an illustration of the proposed method.