Volume 29, Issue 1
A CFD-Aided Galerkin Method for Global Linear Instability Analysis

Shengqi Zhang, Zhenhua XiaShiyi Chen

Commun. Comput. Phys., 29 (2021), pp. 128-147.

Published online: 2020-11

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  • Abstract

Global linear instability analysis is a powerful tool for the complex flow diagnosis. However, the methods used in the past would generally suffer from some disadvantages, either the excessive computational resources for the low-order methods or the tedious mathematical derivations for the high-order methods. The present work proposed a CFD-aided Galerkin methodology which combines the merits from both the low-order and high-order methods, where the expansion on proper basis functions is preserved to ensure a small matrix size, while the differentials, incompressibility constraints and boundary conditions are realized by applying the low-order linearized Navier-Stokes equation solvers on the basis functions on a fine grid. Several test cases have shown that the new method can get satisfactory results for one-dimensional, two-dimensional and three-dimensional flow problems and also for the problems with complex geometries and boundary conditions.

  • Keywords

Global linear instability, spatial discretization, Galerkin method.

  • AMS Subject Headings

76Exx

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-29-128, author = {Zhang , Shengqi and Xia , Zhenhua and Chen , Shiyi}, title = {A CFD-Aided Galerkin Method for Global Linear Instability Analysis}, journal = {Communications in Computational Physics}, year = {2020}, volume = {29}, number = {1}, pages = {128--147}, abstract = {

Global linear instability analysis is a powerful tool for the complex flow diagnosis. However, the methods used in the past would generally suffer from some disadvantages, either the excessive computational resources for the low-order methods or the tedious mathematical derivations for the high-order methods. The present work proposed a CFD-aided Galerkin methodology which combines the merits from both the low-order and high-order methods, where the expansion on proper basis functions is preserved to ensure a small matrix size, while the differentials, incompressibility constraints and boundary conditions are realized by applying the low-order linearized Navier-Stokes equation solvers on the basis functions on a fine grid. Several test cases have shown that the new method can get satisfactory results for one-dimensional, two-dimensional and three-dimensional flow problems and also for the problems with complex geometries and boundary conditions.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2020-0041}, url = {http://global-sci.org/intro/article_detail/cicp/18425.html} }
TY - JOUR T1 - A CFD-Aided Galerkin Method for Global Linear Instability Analysis AU - Zhang , Shengqi AU - Xia , Zhenhua AU - Chen , Shiyi JO - Communications in Computational Physics VL - 1 SP - 128 EP - 147 PY - 2020 DA - 2020/11 SN - 29 DO - http://doi.org/10.4208/cicp.OA-2020-0041 UR - https://global-sci.org/intro/article_detail/cicp/18425.html KW - Global linear instability, spatial discretization, Galerkin method. AB -

Global linear instability analysis is a powerful tool for the complex flow diagnosis. However, the methods used in the past would generally suffer from some disadvantages, either the excessive computational resources for the low-order methods or the tedious mathematical derivations for the high-order methods. The present work proposed a CFD-aided Galerkin methodology which combines the merits from both the low-order and high-order methods, where the expansion on proper basis functions is preserved to ensure a small matrix size, while the differentials, incompressibility constraints and boundary conditions are realized by applying the low-order linearized Navier-Stokes equation solvers on the basis functions on a fine grid. Several test cases have shown that the new method can get satisfactory results for one-dimensional, two-dimensional and three-dimensional flow problems and also for the problems with complex geometries and boundary conditions.

Shengqi Zhang, Zhenhua Xia & Shiyi Chen. (2020). A CFD-Aided Galerkin Method for Global Linear Instability Analysis. Communications in Computational Physics. 29 (1). 128-147. doi:10.4208/cicp.OA-2020-0041
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