Title: Development of a 2-D convection model to simulate phase transition accurately over long time integration* Speaker: Katherine J. Evans, Los Alamos National Laboratory Date/Time: Monday, December 19, 2005, 10:00-11:00 am Location: Building 980, Room 95 (Sandia NM) Brief Abstract: We present a two-dimensional convection phase change model using the incompressible Navier-Stokes equation set and enthalpy as the energy conservation variable. Major algorithmic challenges such as stiff nonlinearities at the phase front are posed by adding self-consistent convection. The equation set is solved with the Jacobian-Free Newton-Krylov (JFNK) nonlinear inexact Newton's method. The generalized-minimum residual (GMRES) algorithm is the linear Krylov solution approximation for the outer Newton loop. SIMPLE, a pressure-correction algorithm, is used as a physics-based preconditioner for GMRES. This algorithm is compared to solutions using SIMPLE as the main solver. Algorithm performance is assessed for a benchmark problem, phase change convection within a square cavity of a solid pure material cooled below the melting temperature. A time step convergence analysis demonstrates that the JFNK model is second order accurate in time. A Gallium melting simulation is also performed and evaluated; in this configuration multiple roll cells develop in the melted region at early times when the aspect ratio is high. The use of spatial discretization greater than first order is necessary to capture the multiple cellular structure and subsequent phase front variations. The JFNK-SIMPLE solution algorithm converges with greater efficiency than SIMPLE as a stand alone solver, and the effect becomes more pronounced for problems with increased size and complexity. JFNK-SIMPLE can provide second order accurate converged solutions to the nonlinear equation set with larger time steps and finer grids than SIMPLE, which performs sequential linear solves on each equation. There are advantages to using SIMPLE solvers, for example their ease of convergence to a linear tolerance. When SIMPLE is incorporated as a preconditioner to JFNK, these benefits are retained, plus the ability to model more complex and realistic problems with minimal and quantified error. *Katherine J. Evans and Dana A. Knoll, Fluid Dynamics Group, T-3 Michael Pernice, |