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Zangeneh, Reza; Ollivier-Gooch, Carl F.

Boundary condition optimization to improve the stability of inviscid and compressible finite-volume methods on unstructured meshes. (English) Zbl 1519.76196

Comput. Fluids 199, Article ID 104418, 18 p. (2020).
Summary: The purpose of this paper is two-fold; first, a systematic approach is developed to improve the steady state stability of cell-centered finite volume methods on unstructured meshes by optimizing boundary conditions. This approach uses the rightmost eigenpairs of the spatially discretized system of equations to determine the existence or the path to stability. This will ensure the energy stability of the system, consequently resulting in convergence to a steady state solution. To this end, it exploits first order gradients of eigenvalues with respect to the types of boundary conditions. This in turn helps in finding an optimized boundary condition type which stabilizes the steady state stability as well as expediting the convergence to the steady state for already stable problems. Secondly, the sensitivity of the rightmost eigenvalues to the solution is measured to investigate the effect of using surrogate or half-converged solutions for the purpose of linearizing the semi-discretized Jacobian.

Cited in 1 Document

MSC:

76M12 Finite volume methods applied to problems in fluid mechanics

Keywords:

spectral stability analysis; energy stability; eigen-analysis; eigenvalue derivatives; numerical boundary conditions; finite volume

Software:

PETSc
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Full Text: DOI

References:

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