On Godunov-type methods for gas dynamics
SIAM Journal on Numerical Analysis
A Cartesian grid embedded boundary method for Poisson's equation on irregular domains
Journal of Computational Physics
Combined immmersed-boundary finite-difference methods for three-dimensional complex flow simulations
Journal of Computational Physics
Journal of Computational Physics
Non-Linear Finite Element Analysis of Solids and Structures: Essentials
Non-Linear Finite Element Analysis of Solids and Structures: Essentials
An immersed-boundary finite-volume method for simulations of flow in complex geometries
Journal of Computational Physics
Journal of Computational Physics
A ghost-cell immersed boundary method for flow in complex geometry
Journal of Computational Physics
Journal of Computational Physics
A Second Order Accurate Embedded Boundary Method for the Wave Equation with Dirichlet Data
SIAM Journal on Scientific Computing
An immersed boundary method for complex incompressible flows
Journal of Computational Physics
Journal of Computational Physics
Derivation and validation of a novel implicit second-order accurate immersed boundary method
Journal of Computational Physics
Hi-index | 31.45 |
Embedded Boundary Methods (EBMs) for Computational Fluid Dynamics (CFD) are usually constructed in the Eulerian setting. They are particularly attractive for complex Fluid-Structure Interaction (FSI) problems characterized by large structural motions and deformations. They are also critical for flow problems with topological changes and FSI problems with cracking. For all of these problems, the alternative Arbitrary Lagrangian-Eulerian (ALE) methods are often unfeasible because of the issue of mesh crossovers. However for viscous flows, Eulerian EBMs for CFD do not track the boundary layers around dynamic rigid or flexible bodies. Consequently, the application of these methods to viscous FSI problems requires either a high mesh resolution in a large part of the computational fluid domain, or adaptive mesh refinement. Unfortunately, the first option is computationally inefficient, and the second one is labor intensive. For these reasons, an alternative approach is proposed in this paper for maintaining all moving boundary layers resolved during the simulation of a turbulent FSI problem using an EBM for CFD. In this approach, which is simple and computationally reasonable, the underlying non-body-fitted mesh is rigidly translated and/or rotated in order to track the rigid component of the motion of the dynamic obstacle. Then, the flow computations away from the embedded surface are performed using the ALE framework, and the wall boundary conditions are treated by the chosen Eulerian EBM for CFD. Hence, the solution of the boundary layer tracking problem proposed in this paper can be described as an ALE implementation of a given EBM for CFD. Its basic features are illustrated with the Large Eddy Simulation using a non-body-fitted mesh of a turbulent flow past an airfoil in heaving motion. Its strong potential for the solution of challenging FSI problems at reasonable computational costs is also demonstrated with the simulation of turbulent flows past a family of highly flexible flapping wings.