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Keywords:

  • Finite volume schemes;
  • defect corrections;
  • WENO reconstruction on unstructured meshes;
  • high-order accuracy;
  • advection diffusion reaction equations;
  • steady state.

Abstract

For the approximation of steady state solutions, we propose an iterated defect correction approach to achieve higher-order accuracy. The procedure starts with the steady state solution of a low-order scheme, in general a second order one. The higher-order reconstruction step is applied a posteriori to estimate the local discretization error of the lower-order finite volume scheme. The defect is then used to iteratively shift the basic lower-order scheme to the desired higher-order accuracy given by the polynomial reconstruction. Hence, instead of solving the high-order discrete equations the low-order basic scheme is solved several times. This avoids that the high-order reconstruction with a large stencil has to be implemented into an existing basic solver and can be seen as a non-intrusive approach to higher-order accuracy.