An improved ghost‐cell immersed boundary method for compressible flow simulations

Abstract

SUMMARYThis study presents an improved ghost-cell immersed boundary approach to represent a solid body in compressible flow simulations. In contrast to the commonly used approaches, in the present work ghost cells are mirrored through the boundary described using a level-set method to farther image points, incorporating a higher-order extra/interpolation scheme for the ghost cell values. A sensor is introduced to deal with image points near the discontinuities in the flow field. Adaptive mesh refinement (AMR) is used to improve the representation of the geometry efficiently in the Cartesian grid system. The improved ghost-cell method is validated against four test cases: (a) double Mach reflections on a ramp, (b) smooth Prandtl-Meyer expansion flows, (c) supersonic flows in a wind tunnel with a forward-facing step, and (d) supersonic flows over a circular cylinder. It is demonstrated that the improved ghost-cell method can reach the accuracy of second order in L 1 norm and higher than first order in L ∞ norm. Direct comparisons against the cut-cell method demonstrate that the improved ghost-cell method is almost equally accurate with better efficiency for boundary representation in high-fidelity compressible flow simulations.

An immersed boundary solver for inviscid compressible flows

“…With the approaches provided in the last 2 subsections, both the Dirichlet and Neumann boundary conditions can be enforced in the ghost points via the approximation along the line normal to the solid wall. In traditional method, 22,26 the boundary conditions for compressible inviscid flow past solid problems are…”

“…For implementation, the layer number of the ghost points depends on the numerical schemes. [20][21][22] However, we have found that using the points far from the surface will increase the error caused by the extrapolation especially when more than one layer of the ghost points are involved for imposing the boundary conditions. The unknown variables of the ghost points are calculated by the symmetrically mirrored points, while the variables at the mirror points can be obtained through the interpolation of the surrounding fluid point.…”

“…We can reconstruct the variables at these ghost cells by using farther points in the fluid domain to get the complete bilinear interpolations at the mirror points. [20][21][22] However, we have found that using the points far from the surface will increase the error caused by the extrapolation especially when more than one layer of the ghost points are involved for imposing the boundary conditions. On the other hand, Mittal et al 3 and Ghias et al 17 use a different approach by introducing the body-intercept (BI) point to build a complete bilinear/trilinear interpolation.…”

Constrained moving least‐squares immersed boundary method for fluid‐structure interaction analysis

“…As shown in Figure , all of the above‐mentioned flow structures are well captured by the present method. We refer to Woodward and Colella and Chi et al for similar results obtained with a grid‐aligned method.…”

“…The computed results for the mass density along the wedge surface are shown in Figure for simulations performed using 400 × 200, 500 × 250, 600 × 300, and 800 × 400 uniform grids. The presently computed results are compared with the grid‐aligned solutions of Chi et al who used a rotational transformation technique and assumed that the shock wave moves at an angle of 60° to the x 1 ‐axis and the domain boundary at the bottom is reflective from x = 1/6. This configuration does not require dealing with the cut‐cell problem of the wedge surface and can be used as a reference for comparison.…”