Efficient monolithic immersed boundary projection methods (MIBPMs) with staggered time discretization have been proposed for incompressible viscous flows with heat transfer. The main idea is to use a two-step approximate lower-upper decomposition technique to decouple the momentum and energy equations, including immersed boundary forcing. The momentum and energy forcing are treated as Lagrangian multipliers to impose divergence-free constraints and no-slip conditions at the immersed boundary surfaces. A staggered time discretization is applied with the Crank-Nicolson scheme to decouple the temperature and velocities, which means that the velocity fields are described at integer time levels (n+1), while the temperature fields are described at half-integer time levels (n+1/2). To investigate the effect of forcing schemes in monolithic formulation, several MIBPM variants based on forcing schemes are formulated and evaluated numerically. The proposed MIBPM presents an accurate imposition of no-slip conditions on the immersed boundary surface and exhibits good stability for two-dimensional forced and natural convection problems. Further, simulations with the proposed MIBPM are implemented for the three-dimensional natural convection problem. Numerical simulation results for single- and multi-particle sedimentation demonstrate the robustness of the proposed method for complex heat transfer flows over moving objects.
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All Science Journal Classification (ASJC) codes
- Numerical Analysis
- Modelling and Simulation
- Physics and Astronomy (miscellaneous)
- General Physics and Astronomy
- Computer Science Applications
- Computational Mathematics
- Applied Mathematics