The present paper describes the development of a novel and comprehensive computational framework to simulate solidification problems in materials processing, specifically casting processes. Heat transfer, solidification and fluid flow due to natural convection are modeled. Empirical relations are used to estimate the microstructure parameters and mechanical properties. The fractional step algorithm is modified to deal with the numerical aspects of solidification by suitably altering the coefficients in the discretized equation to simulate selectively only in the liquid and mushy zones. This brings significant computational speed up as the simulation proceeds. Complex domains are represented by unstructured hexahedral elements. The algebraic multigrid method, blended with a Krylov subspace solver is used to accelerate convergence. State of the art uncertainty quantification technique is included in the framework to incorporate the effects of stochastic variations in the input parameters. Rigorous validation is presented using published experimental results of a solidification problem.

Original languageEnglish (US)
Pages (from-to)132-150
Number of pages19
JournalApplied Mathematical Modelling
StatePublished - Oct 2019


  • Casting
  • Finite volume method
  • Solidification
  • Uncertainty quantification
  • Unstructured grid
  • Validation

ASJC Scopus subject areas

  • Modeling and Simulation
  • Applied Mathematics


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