A Galerkin/POD Reduced-Order Model from Eigenfunctions of Non-Converged Time Evolution Solutions in a Convection Problem

被引：5
|
作者：
Cortes, Jesus [1 ]
Herrero, Henar [1 ]
Pla, Francisco [1 ]
机构：
[1] Univ Castilla La Mancha, Fac Ciencias & Tecnol Quim, Dept Matemat, Ciudad Real 13071, Spain
来源：
MATHEMATICS | 2022年 / 10卷 / 06期
关键词：
reduced-order models; proper orthogonal decomposition; spectral methods; Rayleigh-Benard instability; geophysical flows; TEMPERATURE-DEPENDENT VISCOSITY; POSTERIORI ERROR ESTIMATION; BASIS APPROXIMATION; INERTIAL MANIFOLDS; POD; REDUCTION; EQUATION; FRAMEWORK;
D O I：
10.3390/math10060905
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
A Galerkin/POD reduced-order model from eigenfunctions of non-converged time evolution transitory states in a problem of Rayleigh-Benard is presented. The problem is modeled in a rectangular box with the incompressible momentum equations coupled with an energy equation depending on the Rayleigh number R as a bifurcation parameter. From the numerical solution and stability analysis of the system for a single value of the bifurcation parameter, the whole bifurcation diagram in an interval of values of R is obtained. Three different bifurcation points and four types of solutions are obtained with small errors. The computing time is drastically reduced with this methodology.
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页数：31
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