Improvements of efficiency of finite element simulations of solidification due to adaptive mesh refinement and time-step selection

Arkadiusz Nagórka

Politechnika Częstochowska.

DOI:

https://doi.org/10.7494/cmms.2004.1.0048

Abstract:

The paper deals with an application of adaptive mesh refinement and automatic time-step selection techniques to numerical simulations of solidification. High cooling and heating rates in the beginning of the process involve the need for using very small time steps. Moreover, regions of highest error in the cast subdomain often coincide with the moving fronts of phase change which makes it impossible to generate a common mesh suitable for the entire simulation. In order to avoid high cost of computations on fine and uniform spatial and temporal discretizations adaptivity based on error estimates was introduced to our finite element code. Error of spatial discretization, measured in energy norm, is estimated either by means of a Zienkiewicz-Zhu type error estimator based on postprocessed heat flux or by an explicit residual method. Error estimates form the basis for adaptive mesh refinement. Local truncation error of the time-stepping scheme, estimated by a method utilizing two helper solutions obtained with a smaller time step, allows to select a new step size leading to the solution with accuracy close to preassigned tolerance. Results of example simulations of solidification confirm considerable reduction of computation time thanks to mesh refinement and automatic time-step selection.

Cite as:

Nagórka, A. (2004). Improvements of efficiency of finite element simulations of solidification due to adaptive mesh refinement and time-step selection. Computer Methods in Materials Science, 4(1-2), 8 – 22. https://doi.org/10.7494/cmms.2004.1.0048

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