An immersed boundary method for solving compressible flow with arbitrarily irregular and moving geometry

TL;DR

This paper introduces a new immersed boundary method capable of accurately and efficiently handling complex, irregular, and moving geometries in compressible flow simulations using Cartesian grids.

Contribution

A novel second-order flow reconstruction scheme combined with a fluid-solid coupling framework for improved boundary condition enforcement in complex geometries.

Findings

Accurately handles stationary and moving objects in flow simulations.

Works effectively with convex and concave geometries.

Supports subsonic and supersonic flow conditions.

Abstract

In this paper, a novel immersed boundary method is developed, validated, and applied. Through devising a second-order three-step flow reconstruction scheme, the proposed method is able to enforce the Dirichlet, Neumann, Robin, and Cauchy boundary conditions in a straightforward and consistent manner. Equipped with a fluid-solid coupling framework that integrates high-order temporal and spatial discretization schemes, numerical experiments concerning flow involving stationary and moving objects, convex and concave geometries, no-slip and slip wall boundary conditions, as well as subsonic and supersonic motions are conducted to validate the method. It is demonstrated that the proposed method can provide efficient, accurate, and robust boundary treatment for solving flow with arbitrarily irregular and moving geometries on Cartesian grids.