An efficient ghost-cell immersed boundary method (GCIBM) for simulating turbulent flows in complex geometries is presented. A boundary condition is enforced through a ghost cell method. The reconstruction procedure allows systematic development of numerical schemes for treating the immersed boundary while preserving the overall second-order accuracy of the base solver. Both Dirichlet and Neumann boundary conditions can be treated. The current ghost cell treatment is both suitable for staggered and non-staggered Cartesian grids. The accuracy of the current method is validated using flow past a circular cylinder and large eddy simulation of turbulent flow over a wavy surface. Numerical results are compared with experimental data and boundary-fitted grid results. The method is further extended to an existing ocean model (MITGCM) to simulate geophysical flow over a three-dimensional bump. The method is easily implemented as evidenced by our use of several existing codes.

A Ghost-Cell Immersed Boundary Method for Flow in Complex Geometry

The present study investigates the shock wave interactions involving stationary and moving wedges using a sharp interface immersed boundary method combined with a fifth-order weighted essentially non-oscillatory scheme. Inspired by Schardin’s problem, which involves moving shock interaction with a finite triangular wedge, we study the influence of incident shock Mach numbers and corner angles on the resulting flow physics under both stationary and moving conditions. The present study involves three incident shock Mach numbers (1.3, 1.9, and 2.5) and three corner angles (60°, 90°, and 120°), while its impact on the vorticity production is investigated using the vorticity transport equation, circulation, and rate of circulation production. Furthermore, the results yield that the generation of the vorticity due to the viscous effects is quite dominant compared to the baroclinic or compressibility effects. The moving cases presented involve shock driven wedge problems. The fluid and wedge structure dynamics are coupled using the Newtonian equation. These shock driven wedge cases show that wedge acceleration due to the shock results in a change in reflected wave configuration from single Mach reflection to double Mach reflection. The intermediary state between them, the transition Mach reflection, is also observed in the process. The effect of shock Mach numbers and corner angles on the triple point trajectory, as well as on the drag coefficient, is analyzed in this study.

Investigation of shock wave interactions involving stationary and moving wedges

Development of a high-order continuous Galerkin sharp-interface immersed boundary method and its application to incompressible flow problems

We present a robust and efficient sharp interface immersed boundary (IBM) framework, which is applicable for all-speed flow regimes and is capable of handling arbitrarily complex bodies (stationary or moving). We use an in-house, parallel, multi-block structured finite volume flow solver, which employs a 3D unsteady Favre averaged Navier Stokes equations in a generalized curvilinear coordinate system. The discretization of inviscid fluxes involves a low diffusion flux splitting scheme, while it invokes a second-order central differencing for viscous fluxes. The immersed body is represented by unstructured triangular meshes, and the interface boundary conditions are satisfied by reconstructing the flow field near the immersed surface. We employ a combination of HCIB (Hybrid Cartesian Immersed boundary) method and GC(Ghost-cell) for solution reconstruction, while the interface tracking procedure is based on ray tracing algorithm and a novel three step solution reconstruction procedure that computes pseudo-normals in the regions where the normal is not well-defined and reconstructs the flow field along those directions. We demonstrate that this procedure enables solver to efficiently handle and accurately represent sharp-edged regions. Issues of mass conservation and spurious temporal oscillations are handled using ghost-cell based field extension technique. The developed IBM framework is applied to a wide range of flow phenomena encompassing all-speed regimes (M=0.001 to M = 2.0).

A Robust and Efficient Sharp Interface Immersed Boundary Framework for Viscous Flow Simulations at Arbitrary Mach Number Involving Complex and Moving Boundaries

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A Robust and Efficient Sharp Interface Immersed Boundary Framework for Viscous Flow Simulations at Arbitrary Mach Number Involving Complex and Moving Boundaries