论文标题
不可压缩的Navier-Stokes方程的动量支持ROM
Momentum-conserving ROMs for the incompressible Navier-Stokes equations
论文作者
论文摘要
基于投影的模型订单降低了普通微分方程（ODE）导致投影ode。基于此ODE，有限体积离散化的现有缩减模型（ROM）满足了对任意选择的子域的基本保护法。但是，此ROM不能完全满足预测的颂歌，而是引入了额外的扰动术语。在这项工作中，我们提出了一个具有相同子域保护特性的新型ROM，确实可以完全满足预测的颂歌。 我们将此ROM应用于不可压缩的Navier-Stokes方程，并显示了质量方程式如何构建新颖的ROM以满足代数约束。 此外，我们表明，由此产生的质量支持ROM使我们能够得出动能能量保护并因此是非线性稳定性，由于存在扰动项，现有ROM是不可能的。
Projection-based model order reduction of an ordinary differential equation (ODE) results in a projected ODE. Based on this ODE, an existing reduced-order model (ROM) for finite volume discretizations satisfies the underlying conservation law over arbitrarily chosen subdomains. However, this ROM does not satisfy the projected ODE exactly but introduces an additional perturbation term. In this work, we propose a novel ROM with the same subdomain conservation properties which indeed satisfies the projected ODE exactly. We apply this ROM to the incompressible Navier-Stokes equations and show with regard to the mass equation how the novel ROM can be constructed to satisfy algebraic constraints. Furthermore, we show that the resulting mass-conserving ROM allows us to derive kinetic energy conservation and consequently nonlinear stability, which was not possible for the existing ROM due to the presence of the perturbation term.
