Abstract
From the analysis of solidification based on the energy transport equation presented in the previous section, it was seen that analytical solutions of this equation are not always available. Significant simplifying assumptions must be used, assumptions that are many times debilitating to the point that the solution is of little engineering interest. Fortunately, with the development of numerical methods and their application to the solution of partial differential equations, the most complicated equations can be solved numerically. Numerical solutions rely on replacing the continuous information contained in the exact solution of the differential equation with discrete values. Discretization equations are derived from the governing differential equation.
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Stefanescu, D.M. (2002). Macro-Modeling of Solidification. Numerical Approximation Methods. In: Science and Engineering of Casting Solidification. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-6472-7_6
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DOI: https://doi.org/10.1007/978-1-4757-6472-7_6
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