Numerical Analysis of an Efficient Time Integration Scheme for Unsteady Conjugate Heat Transfer

The computational results of a time integration method for thermal interaction between viscous gas flows and solid domains are presented. The methodology is based on simultaneous integration of the multicomponent gas dynamics equations and the thermal conductivity equation of a solid domain. For three-dimensional spatial discretization of the governing equations, multi-block unstructured grids with definition of grid functions at grid nodes are used. On each time step, the governing system is split into hyperbolic and parabolic subsystems. The numerical method provides an approximation of the fluid-solid interface condition (both normal heat flux and temperature are continuous across the interface). To analyze the accuracy and computational efficiency of the scheme, a model problem of high-speed laminar flow around a heated plate is considered. The numerical results demonstrate good agreement with analytical solution and confirm the effectiveness of the developed methodology.