An improved immersed boundary method with local flow pattern reconstruction and its validation

This study introduces an immersed boundary (IB) method based on coefficient array transformations of discrete equations for local cells and local flow pattern reconstruction, for the simulation of turbulent flow and combustion chemistry inside combustors with complex structure. This IB method is combined with a geometric scanning algorithm that traverses each fluid grid point in the vicinity of the wall, and based on the exact wall positions and normal vectors obtained from the scanning, the coefficient matrices of the individual grid points and their discrete forms of the governing equations are transformed, and the boundary conditions are added implicitly and exactly. The effectiveness of the method is validated through simulations of a cylinder, a gas turbine model combustor [Meier et al., "Spray and flame structure of a generic injector at aeroengine conditions," in Proceedings of the ASME 2011 Turbo Expo: Power for Land, Sea, and Air (American Society of Mechanical Engineers, 2011), pp. 61-72 and Freitag et al., "Measurement of initial conditions of a kerosene spray from a generic aeroengine injector at elevated pressure," Atomization Sprays 21, 521 (2011)], and a specific aero-engine combustor, demonstrating precision comparable to traditional body-fitted mesh approaches, especially for complex combustor structures. The simulation demonstrates that the IB method achieves accuracy comparable to a fitted grid when it provides boundary information of similar quality and detail for control equations. The locally reconstructed IB method introduced in this paper successfully delivers high-precision boundary conditions, making it valuable for practical engineering applications.