Abstract 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.

中文翻译：

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边界条件优化以提高无粘性和可压缩有限体积方法在非结构网格上的稳定性

摘要 本文的目的有两个：首先，开发了一种系统方法，通过优化边界条件来提高非结构网格上以单元为中心的有限体积方法的稳态稳定性。这种方法使用空间离散方程组的最右边的特征对来确定存在性或稳定性的路径。这将确保系统的能量稳定性，从而导致收敛到稳态解。为此，它利用与边界条件类型相关的特征值的一阶梯度。这反过来有助于找到优化的边界条件类型，该类型可以稳定稳态稳定性，并加速已经稳定的问题收敛到稳态。第二，