A Direct-Forcing Immersed Boundary Projection Method for Thermal Fluid-Solid Interaction Problems (Advances in Applied Mathematics and Mechanics, 2022)
In this paper, we develop a direct-forcing immersed boundary projectionmethod for simulating the dynamics in thermal fluid-solid interaction problems. Theunderlying idea of the method is that we treat the solid as made of fluid and introduce two virtual forcing terms. First, a virtual fluid force distributed only on the solidregion is appended to the momentum equation to make the region behave like a realsolid body and satisfy the prescribed velocity. Second, a virtual heat source locatedinside the solid region near the boundary is added to the energy transport equation toimpose the thermal boundary condition on the solid boundary. We take the implicitsecond-order backward differentiation to discretize the time variable and employ theChoi-Moin projection scheme to split the coupled system. As for spatial discretization,second-order centered differences over a staggered Cartesian grid are used on the entire domain. The advantages of this method are its conceptual simplicity and easeof implementation. Numerical experiments are performed to demonstrate the highperformance of the proposed method. Convergence tests show that the spatial convergence rates of all unknowns seem to be super-linear in the 1-norm and 2-norm whileless than linear in the maximum norm.