Abstract
In this article we apply the procedure of the iterated defect correction method to the Euler equations as well as to the Navier-Stokes equations. One building block in the defect correction approach is the lower order basic method, usually first or second order accurate. This scheme gives a steady solution of low accuracy as the starting point. The second building block is the WENO reconstruction step to estimate the local defect. The local defect is put into the original equation as source on the right hand side with a minus sign. The resulting modified equation is then again solved with the low order scheme. Due to the source term with the local defect the order of accuracy is iteratively shifted to the order of the reconstruction. We show numerical results for several validation test cases and applications.
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Filimon, A., Munz, CD. (2013). The Application of Iterated Defect Corrections Based on WENO Reconstruction. In: Eisfeld, B., Barnewitz, H., Fritz, W., Thiele, F. (eds) Management and Minimisation of Uncertainties and Errors in Numerical Aerodynamics. Notes on Numerical Fluid Mechanics and Multidisciplinary Design, vol 122. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36185-2_6
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DOI: https://doi.org/10.1007/978-3-642-36185-2_6
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