A Non-Body Conformal Grid Method for Simulation of Compressible Flows with Complex Immersed Boundaries

Abstract

A compressible non-body conformal grid method is presented. The method is designed to simulate a large variety of subsonic compressible flows with complex geometries. A hybrid implicit-explicit timediscretization scheme is chosen. The diagonal viscous terms are treated implicitly and all other terms including the convective terms and cross-terms are treated explicitly using a low-storage, 3 rd-Order Runge-Kutta scheme. A mixed second-order central difference-QUICK scheme has been used which allows us to precisely control the numerical damping. A ghostcell approach is employed in conjunction with a bilinear interpolation scheme so as to satisfy the boundary conditions on the immersed boundaries while preserving second-order accuracy. Numerical results are validated by comparing against experimental data and other established simulation results.

A versatile sharp interface immersed boundary method for incompressible flows with complex boundaries

“…The second sub-step requires the solution of the pressure correction equation (9) which is solved with the constraint that the final velocity be divergence-free. This gives the following Poisson equation for the pressure correction (10) and a Neumann boundary condition imposed on this pressure correction at all boundaries. This Poisson equation is solved with a highly efficient geometric multigrid method [3] which employs a Gauss-Siedel line-SOR smoother [38].…”

“…The current immersed boundary method employs a multi-dimensional ghost-cell methodology to impose the boundary conditions on the immersed boundary and is similar in spirit to the methodology proposed by Majumdar et al [21] and employed by Ghias et al [10,11] among others. However, unlike these previous efforts, the current solver is designed from the start for fast, efficient and accurate solution of flows with complex three-dimensional, moving boundaries.…”

“…(24) is used as the velocity boundary condition in advancing the flow equations (Eqs. [3][4][5][6][7][8][9][10][11][12][13] which ensures that at the end of the time-step, the boundary and flow velocities are compatible. The general framework described above can therefore be considered as EulerianLagrangian, wherein the immersed boundaries are explicitly tracked as surfaces in a Lagrangian mode, while the flow computations are performed on a fixed Eulerian grid.…”

A Brinkman penalization method for compressible flows in complex geometries

“…The Cartesian grid method [17] was used to simulate the compressible flows around a circular cylinder and an airfoil at high Reynolds numbers by directly modifying the discretized equations near the immersed boundaries. However, the acoustic wave reflection and transmission at the interface between fluid and solid media had not been taken into account, which are critical in some applications with acoustic and shock wave propagation around solid obstacles.…”

Low Dimensional Modeling for Zero-Net Mass-Flux Actuators

“…26 The schematic in Fig. 5 (a) shows a solid body with a curved boundary moving through a fluid and the categorization of the nodes for the purpose of implementing the ghost cell methodology.…”