Temporal accuracy analysis of phase change convection simulations using the JFNK-SIMPLE algorithm. (English) Zbl 1388.76246

Evans, Katherine J.; Knoll, Dana A.

Int. J. Numer. Methods Fluids 55, No. 7, 637-653 (2007).

Summary: The incompressible Navier-Stokes and energy conservation equations with phase change effects are applied to two benchmark problems: (1) non-dimensional freezing with convection; and (2) pure gallium melting. Using a Jacobian-free Newton-Krylov (JFNK) fully implicit solution method preconditioned with the SIMPLE [S. V. Patankar, Numerical heat transfer and fluid flow. Washington – New York – London: Hemisphere Publishing Corporation; New York etc.: McGraw-Hill Book Company (1980; Zbl 0521.76003)] algorithm using centred discretization in space and three-level discretization in time converges with second-order accuracy for these problems. In the case of non-dimensional freezing, the temporal accuracy is sensitive to the choice of velocity attenuation parameter. By comparing to solutions with first-order backward Euler discretization in time, it is shown that the second-order accuracy in time is required to resolve the fine-scale convection structure during early gallium melting. Qualitative discrepancies develop over time for both the first-order temporal discretized simulation using the JFNK-SIMPLE algorithm that converges the nonlinearities and a SIMPLE-based algorithm that converges to a more common mass balance condition. The discrepancies in the JFNK-SIMPLE simulations using only first-order rather than second-order accurate temporal discretization for a given time step size appear to be offset in time.

MSC:

76M25	Other numerical methods (fluid mechanics) (MSC2010)
80M25	Other numerical methods (thermodynamics) (MSC2010)
76R10	Free convection

Keywords:

Newton-Krylov methods; temporal accuracy; time step convergence; gallium melting; SIMPLE preconditioner; phase change convection

Citations:

Zbl 0521.76003

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