Session B3 - Symbolic Analysis
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On Strongly Consistent Finite Difference Approximations to the Navier-Stokes Equations
KAUST, KSA - firstname.lastname@example.org
The finite difference method is widely used for solving partial differential equations in the computational sciences. The decisive factor for its successful application is the quality of the underlying finite difference approximations. In this contribution, we present a computer algebra assisted approach to generate appropriate finite difference approximations to systems of polynomially nonlinear partial differential equations on regular Cartesian grids. The generated approximations satisfy the major quality criterion -- strong consistency -- which implies the preservation of fundamental algebraic properties of the system at the discrete level. This criterion admits a verification algorithm. We apply our approach to the Navier-Stokes equations and construct strongly consistent approximations. Moreover, we construct two approximations which are not only strongly consistent but also fully conservative.
Joint work with Vladimir Gerdt (JINR, Russia) and Dominik Michels (KAUST, KSA).