Stability of Navier–Stokes discretizations on collocated meshes of high anisotropy and the performance of algebraic multigrid solvers

This paper describes the development and validation steps of a characteristics-based explicit along with a novel fully implicit mixing plane implementation for turbomachinery applications. The framework is an unstructured 3D RANS in-house modified solver, based on open-source libraries. Particular attention was paid to mass-conservation, accurate variables interpolation, and algorithm stability in order to improve robustness and convergence. By introducing a specific interface, allowing the use of algebraic multigrid solvers together with multiprocessor computation, a speed up of the numerical solution procedure was achieved. The validation of both mixing plane algorithms is carried out on an industrial radial compressor and a cold air 1.5 stages axial turbine.

Download Full-text

Least-Squares Finite Element Methods and Algebraic Multigrid Solvers for Linear Hyperbolic PDEs

SIAM Journal on Scientific Computing ◽

10.1137/s106482750240858x ◽

2004 ◽

Vol 26 (1) ◽

pp. 31-54 ◽

Cited By ~ 28

Author(s):

H. De Sterck ◽

Thomas A. Manteuffel ◽

Stephen F. McCormick ◽

Luke Olson

Keyword(s):

Finite Element ◽

Least Squares ◽

Finite Element Methods ◽

Algebraic Multigrid ◽

Hyperbolic Pdes ◽

Multigrid Solvers

Download Full-text

Accelerating algebraic multigrid solvers on NVIDIA GPUs

Computers & Mathematics with Applications ◽

10.1016/j.camwa.2015.07.005 ◽

2015 ◽

Vol 70 (5) ◽

pp. 1162-1181 ◽

Cited By ~ 5

Author(s):

Hui Liu ◽

Bo Yang ◽

Zhangxin Chen

Keyword(s):

Algebraic Multigrid ◽

Multigrid Solvers

Download Full-text

Algebraic multigrid for the finite pointset method

Computing and Visualization in Science ◽

10.1007/s00791-020-00324-3 ◽

2020 ◽

Vol 23 (1-4) ◽

Author(s):

Bram Metsch ◽

Fabian Nick ◽

Jörg Kuhnert

Keyword(s):

Differential Operators ◽

Stokes Equations ◽

Algebraic Multigrid ◽

Navier Stokes ◽

Symmetric Matrices ◽

Point System ◽

Navier Stokes Equations ◽

Saddle Point System ◽

Matrix Property ◽

Velocity Pressure

AbstractWe investigate algebraic multigrid (AMG) methods for the linear systems arising from the discretization of Navier–Stokes equations via the finite pointset method. In the segregated approach, three pressure systems and one velocity system need to be solved. In the coupled approach, one of the pressure systems is coupled with the velocity system, leading to a coupled velocity-pressure saddle point system. The discretization of the differential operators used in FPM leads to non-symmetric matrices that do not have the M-matrix property. Even though the theoretical framework for many AMG methods requires these properties, our AMG methods can be successfully applied to these matrices and show a robust and scalable convergence when compared to a BiCGStab(2) solver.

Download Full-text