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High‐order ghost‐point immersed boundary method for viscous compressible flows based on summation‐by‐parts operators
Author(s) -
Khalili M. Ehsan,
Larsson Martin,
Müller Bernhard
Publication year - 2018
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.4696
Subject(s) - immersed boundary method , mathematics , cylinder , boundary (topology) , solver , mathematical analysis , interpolation (computer graphics) , flow (mathematics) , moving least squares , compressible flow , geometry , boundary value problem , compressibility , mechanics , physics , mathematical optimization , classical mechanics , motion (physics)
Summary A high‐order immersed boundary method is devised for the compressible Navier‐Stokes equations by employing high‐order summation‐by‐parts difference operators. The immersed boundaries are treated as sharp interfaces by enforcing the solid wall boundary conditions via flow variables at ghost points. Two different interpolation schemes are tested to compute values at the ghost points and a hybrid treatment is used. The first method provides the bilinearly interpolated flow variables at the image points of the corresponding ghost points and the second method applies the boundary condition at the immersed boundary by using the weighted least squares method with high‐order polynomials. The approach is verified and validated for compressible flow past a circular cylinder at moderate Reynolds numbers. The tonal sound generated by vortex shedding from a circular cylinder is also investigated. In order to demonstrate the capability of the solver to handle complex geometries in practical cases, flow in a cross‐section of a human upper airway is simulated.