Nonlinear discretizations are necessary for convection-diffusion equations for obtaining accurate... more Nonlinear discretizations are necessary for convection-diffusion equations for obtaining accurate solutions that satisfy the discrete maximum principle. The numerical solution of the arising nonlinear problems is often difficult. This paper presents several approaches for solving the nonlinear problems of algebraic flux correction (AFC) schemes for the Kuzmin limiter and the BJK limiter. Comprehensive numerical studies are performed at examples that model the transport of energy from a body in a flow field in two and three dimensions. It turns out that the most efficient approach, from the point of view of computing times, is a simple fixed point iteration, because the iteration matrix possesses properties that can be exploited by the solvers of the arising linear systems of equations.
Nonlinear discretizations are necessary for convection-diffusion equations for obtaining accurate... more Nonlinear discretizations are necessary for convection-diffusion equations for obtaining accurate solutions that satisfy the discrete maximum principle. The numerical solution of the arising nonlinear problems is often difficult. This paper presents several approaches for solving the nonlinear problems of algebraic flux correction (AFC) schemes for the Kuzmin limiter and the BJK limiter. Comprehensive numerical studies are performed at examples that model the transport of energy from a body in a flow field in two and three dimensions. It turns out that the most efficient approach, from the point of view of computing times, is a simple fixed point iteration, because the iteration matrix possesses properties that can be exploited by the solvers of the arising linear systems of equations.
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Papers by Volker John