论文标题
稳定的Navier-Stokes方程的两级Galerkin减少订单模型
A Two-Level Galerkin Reduced Order Model for the Steady Navier-Stokes Equations
论文作者
论文摘要
我们提出，分析和研究数值的新型两级盖尔金还原模型（2L-ROM），以对稳定的Navier-Stokes方程进行有效，准确的数值模拟。在2L-ROM的第一步中，求解了相对较低的非维非线性系统。在第二步中，Navier-Stokes方程是在第一步中发现的解决方案周围线性化的，并解决了线性化问题的较高维度系统。我们证明了针对新的2L-ROM绑定的误差，并将其与稳定汉堡方程的数值模拟中的标准一级ROM（1L-ROM）进行了比较。 2L-ROM显着降低（$ 2 $甚至$ 3 $）的1L-ROM计算成本，而不会损害其数值准确性。
We propose, analyze, and investigate numerically a novel two-level Galerkin reduced order model (2L-ROM) for the efficient and accurate numerical simulation of the steady Navier-Stokes equations. In the first step of the 2L-ROM, a relatively low-dimensional nonlinear system is solved. In the second step, the Navier-Stokes equations are linearized around the solution found in the first step, and a higher-dimensional system for the linearized problem is solved. We prove an error bound for the new 2L-ROM and compare it to the standard one level ROM (1L-ROM) in the numerical simulation of the steady Burgers equation. The 2L-ROM significantly decreases (by a factor of $2$ and even $3$) the 1L-ROM computational cost, without compromising its numerical accuracy.
