Development of a horizontal two-dimensional melt spread analysis code, THERMOS-MSPREAD Part-1: Spreading models, numerical solution methods and verifications

This article is the first part of two-part series describing the MSPREAD code developed for analyzing anisotropic melt spreading. The debris bed is modeled as a multi-layer structure consisting of the substrate, melt, upper and bottom crusts, and ambient fluid. The spreading of the debris bed is expressed based on the shallow water equation. The growth of the upper and bottom crusts is modeled. The heat conduction equation is solved in the substrate at the bottom and side walls based on 1D and 3D heat conduction models, respectively. The friction and heat transfer are expressed by closure equations that cover both dry and wet conditions. The numerical solution algorithm was described in the vector form. The fluxes at the cell boundary for the advection terms were expressed using the AUSM(+)-up scheme. The pressure equation is solved by the SIMPLEC method. Since the melt viscosity changes largely as the melt spreads, the viscosity terms are treated implicitly. Four verifications were introduced: two for the shallow water equations solver, one for the crust growth, and one for the side wall heat conduction. The dependences on the cell and time step sizes were studied via comparisons with the exact or higher-order numerical solutions.