Resolving the phase change of glassy materials and the subsequent flow of the molten layer presents a challenging fluid dynamics problem with applications ranging from manufacturing to atmospheric entry. We focus on resolving melt formation of silica glass under high heat flux in the presence of a strong surface shear force inducing motion of the resulting melt over an inert substrate. With excessive heating, we include mass-loss effects due to evaporation. To fully explore the dependence of the flow on applied heat flux and shear force, viscosity, surface tension, and adhesion to the substrate, the fluid-gas interface must be resolved and dynamically tracked through the simulation. Various level-sets are used to describe the different phases present. The Conformal Decomposition Finite Element Method (CDFEM) is used to dynamically decompose a background tetrahedral mesh into conformal material domains resolving the gas, fluid, and solid regions in our test configuration. Formation of the melt is captured through resolving the temperature-dependent viscosity along with suitable volumetric source terms on the energy conservation equation. We explore parametric configurations leading to melt flow, down-stream surface wetting, rivulet formulation and motion, and finally flow separation and droplet formation. Sandia National Laboratories is a multi-mission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-NA0003525.