Non-linearly stable reduced-order models for incompressible flow with energy-conserving finite volume methods

JOURNAL OF COMPUTATIONAL PHYSICS

卷:421

Article

Sanderse, B.¹ 

[1] Ctr Wiskunde & Informat, Amsterdam, Netherlands

关键词: Incompressible Navier-Stokes equations;    Reduced-order model;    Energy conservation;    POD-Galerkin;    Finite volume method;    Stability;   

DOI  :  10.1016/j.jcp.2020.109736

来源: Elsevier

【 摘 要 】

A novel reduced-order model (ROM) formulation for incompressible flows is presented with the key property that it exhibits non-linearly stability, independent of the mesh (of the full order model), the time step, the viscosity, and the number of modes. The two essential elements to non-linear stability are: (1) first discretise the full order model, and then project the discretised equations, and (2) use spatial and temporal discretisation schemes for the full order model that are globally energy-conserving (in the limit of vanishing viscosity). For this purpose, as full order model a staggered-grid finite volume method in conjunction with an implicit Runge-Kutta method is employed. In addition, a constrained singular value decomposition is employed which enforces global momentum conservation. The resulting 'velocity-only' ROM is thus globally conserving mass, momentum and kinetic energy. For non-homogeneous boundary conditions, a (onetime) Poisson equation is solved that accounts for the boundary contribution. The stability of the proposed ROM is demonstrated in several test cases. Furthermore, it is shown that explicit Runge-Kutta methods can be used as a practical alternative to implicit time integration at a slight loss in energy conservation. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

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