Numerical Simulations of Heat Transfer and Fluid Flow Problems Using an Immersed-Boundary Finite-Volume Method on NonStaggered Grids

Study of multiple steady solutions for the 2D natural convection in a concentric horizontal annulus with a constant heat flux wall using immersed boundary-lattice Boltzmann method

“…(8) is replaced by the regularization function Dðx À XÞ in Eq. (29). So the the temperature field can be corrected by…”

“…Their basic idea is introducing the heat source/sink on the body surface or inside to satisfy the temperature boundary condition. Pacheco et al also developed an immersed-boundary finite-volume method on nonstaggered grids to simulate the fluid flow and heat transfer problems [29]. Wang et al considered a multi-direct heat source scheme for the simulation of flows with heat transfer [30].…”

A consistent direct discretization scheme on Cartesian grids for convective and conjugate heat transfer

“…Previous studies have mostly dealt with Dirichlet boundary conditions [21][22][23][24], and there are a limited number of studies that implement Neumann boundary conditions. Pacheco et al [25] and Pacheco-Vega et al [26] proposed a successive determination algorithm of the temperature inside a body to match the prescribed heat flux at the immersed boundary. Zhang et al [27] proposed another implementation of a Neumann boundary condition; the temperature gradient at the boundary is evaluated on layers of Lagrangian points along the body surface.…”

A Three-Dimensional, Immersed Boundary, Finite Volume Method for the Simulation of Incompressible Heat Transfer Flows around Complex Geometries

“…Several works exist in the literature regarding extending IBM approaches to solve the energy equation around complex geometries by imposing Dirichlet and Neumann boundary conditions [19][20][21][22][23][24][25][26][27]. Conjugate heat transfer simulations, where the energy equation is also solved inside the immersed body, using IBM were also reported in [28][29][30][31].…”