An energy-conservative DG-FEM approach for solid–liquid phase change

We present a discontinuous Galerkin method for melting/solidification problems based on the “linearized enthalpy approach,” which is derived from conservative form of energy transport equation and does not depend use so-called mushy zone. symmetric interior penalty Lax–Friedrichs flux to discretize diffusive convective terms, respectively. Time discretized with second-order implicit backward differentiation formula, two outer iterations extrapolation predictors are used coupling momentum energy. The numerical was validated three different benchmark cases, i.e., one-dimensional Stefan problem, octadecane melting in square cavity gallium rectangular cavity. performance quantified L2 norm error number needed convergence at each time step. For all validation mesh rate approximately O(h) obtained, below expected accuracy method. Only case, higher-order proved be beneficial. results campaign demonstrate promise finite element modeling certain solid–liquid phase change where large gradients flow field or highly localized, however, further enhancement fully benefit when solving problems.