A computational strategy for simulating heat transfer and flow past deformable objects Anvar Gilmanov a , Sumanta Acharya b, * a Center for Computations and Technology, Louisiana State University, Baton Rouge, LA 70803, United States b Mechanical Engineering, Louisiana State University, Baton Rouge, LA 70803, United States Received 21 May 2007; received in revised form 13 November 2007 Available online 7 March 2008 Abstract Simulations of flow and heat transfer around deforming objects require the accurate resolution of the moving interface. An approach that combines the Hybrid Immersed Boundary Method (HIBM) for handling complex moving boundaries and the Material Point Method (MPM) for resolving structural stresses and the movement of the deformable body is presented here. In the HIBM, a fixed Eule- rian, curvilinear grid is generally defined, and the variable values at grid points adjacent to a curvilinear boundary are interpolated to satisfy the boundary conditions. The MPM is used to solve equations of the solid structure (stresses and deflection) and communicates with the flow equations through appropriate interface-boundary conditions. As a validation of the new approach for heat transfer prob- lems, flow and heat transfer past a rigid and deforming isothermal sphere is simulated. Predictions agree well with published results of Nusselt number for flow past a rigid sphere. Ó 2008 Elsevier Ltd. All rights reserved. Keywords: Artificial compressibility; Dual time-stepping; Immersed boundaries; Material point method; Fluid–structure interaction; Heat transfer 1. Introduction In many applications involving heat transfer, surfaces that deform under the action of the fluid flow are encoun- tered. These problems which involve fluid–structure interac- tion (FSI) require specific treatment in the vicinity of the interface. Examples include applications in thermal sprays, injection molding, and polymer processing. Numerical approaches for solving FSI problems are broadly classified as: fixed-grid (Eulerian) or moving-grid (Lagrangian or Arbitrary Lagrangian–Eulerian) methods [1]. Fixed-grid methods generally embody a surface-captur- ing strategy [2], and the interface has a non-zero thickness and is diffuse [1]. Moving-grid methods belong to the sur- face-tracking family, since with these approaches the inter- face is maintained to be sharp with an essentially zero thickness. Popular moving-grid methods for solving FSI problems are the Lagrangian [3] and Arbitrary Lagrangi- anEulerian (ALE) methods [4,5]. A purely Lagrangian method was employed by Belytschko and Kennedy [6], and Donea et al. [7] to study hydro-structural interactions. However, ALE methods are more popular, since they use a moving-grid that follows the deforming boundaries and allows the resolution needed near the boundary [4,5,8]. However, due to the need for the mesh to conform to the body at all times, they are inherently limited to problems with moderate body deformations. Fixed-grid approaches have been widely used due to the ease of generating a fixed-grid. Different strategies with a fixed-grid have been proposed. In the Cut-Cell Method [9–15] the boundary cells and fluxes adjacent to the com- plex interface are redefined at each step. In the Volume of Fluid Method (VOF) [16,17] the interface is reconstructed from the fractional volume of fluid content in each cell through special surface functions which are used to distin- guish one fluid from another. Level Set Methods (LSM) were introduced by Osher and Sethian [18] and rely on 0017-9310/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijheatmasstransfer.2007.11.055 * Corresponding author. E-mail address: acharya@me.lsu.edu (S. Acharya). www.elsevier.com/locate/ijhmt Available online at www.sciencedirect.com International Journal of Heat and Mass Transfer 51 (2008) 4415–4426