High‐order stable interpolations for immersed boundary methods

Abstract

SUMMARYThe analysis and improvement of an immersed boundary method (IBM) for simulating turbulent ows over complex geometries are presented. Direct forcing is employed. It consists in interpolating boundary conditions from the solid body to the Cartesian mesh on which the computation is performed. Lagrange and least squares high-order interpolations are considered. The direct forcing IBM is implemented in an incompressible ÿnite volume Navier-Stokes solver for direct numerical simulations (DNS) and large eddy simulations (LES) on staggered grids. An algorithm to identify the body and construct the interpolation schemes for arbitrarily complex geometries consisting of triangular elements is presented. A matrix stability analysis of both interpolation schemes demonstrates the superiority of least squares interpolation over Lagrange interpolation in terms of stability. Preservation of time and space accuracy of the original solver is proven with the laminar two-dimensional Taylor-Couette ow. Finally, practicability of the method for simulating complex ows is demonstrated with the computation of the fully turbulent three-dimensional ow in an air-conditioning exhaust pipe.

Immersed Boundary Method with Artificial Density in Pressure Equation for Modeling Flows Confined by Wall Boundaries

“…We evaluate the absolute error in velocity magnitude at the channel center position between the numerical result and the analytical solution. This measurement is similar to the error analysis for IB by Peller et al (2006). The numerical errors from all three channel geometries are summarized in Figure 5 against the grid resolution.…”

Immersed Boundary Methods for High-Resolution Simulation of Atmospheric Boundary-Layer Flow Over Complex Terrain

“…Balaras [2004] note that the use of a linear eddy viscosity reconstruction is most likely only acceptable because very fine grids are used near the immersed boundary. Peller et al [2006] reconstruct the velocity in the fluid domain using higher-order Lagrange and least squares interpolations. In this method, a higher-order polynomial based on either of the two interpolation methods is used along the surface normal, instead of a linear relationship.…”

A Complementary Numerical / Experimental Investigation on the Flow over Periodic Hills at 100 ≤ Re ≤ 10.595

“…The hill geometry is represented by a triangular mesh. The immersed boundary technique provides a smooth representation of the body surface by using third-order least squares interpolation for the interface cells [5,7].…”