High-order discontinuous Galerkin spectral element methods for transitional and turbulent flow simulations

2014 ◽  
Vol 76 (8) ◽  
pp. 522-548 ◽  
Author(s):  
Andrea D. Beck ◽  
Thomas Bolemann ◽  
David Flad ◽  
Hannes Frank ◽  
Gregor J. Gassner ◽  
...  
Keyword(s):  
Turbulent Flow ◽  
Discontinuous Galerkin ◽  
Spectral Element ◽  
High Order ◽  
Spectral Element Methods ◽  
Flow Simulations

scholarly journals Multi-element SIAC Filter for Shock Capturing Applied to High-Order Discontinuous Galerkin Spectral Element Methods

2019 ◽  
Vol 81 (2) ◽  
pp. 820-844
Author(s):  
Marvin Bohm ◽  
Sven Schermeng ◽  
Andrew R. Winters ◽  
Gregor J. Gassner ◽  
Gustaaf B. Jacobs
Keyword(s):  
Discontinuous Galerkin ◽  
Spectral Element ◽  
High Order ◽  
Shock Capturing ◽  
Spectral Element Methods

Computation of Forward-Time Finite-Time Lyapunov Exponents Using Discontinuous-Galerkin Spectral Element Methods

2013 ◽  
Author(s):  
Daniel A. Nelson ◽  
Gustaaf B. Jacobs
Keyword(s):  
Lyapunov Exponents ◽  
Discontinuous Galerkin ◽  
Finite Time ◽  
Deformation Gradient ◽  
Spectral Element ◽  
High Order ◽  
Exact Equation ◽  
Spectral Element Methods ◽  
Finite Time Lyapunov Exponents ◽  
Flow Map

We present an algorithm for computing forward-time finite-time Lyapunov exponents (FTLEs) using discontinuous-Galerkin (DG) operators. Passive fluid tracers are initialized at Gauss-Lobatto quadrature nodes and advected concurrently with direct numerical simulation (DNS) using DG spectral element methods. The flow map is approximated by a high-order polynomial and the deformation gradient tensor is then determined by the spectral derivative. Since DG operators are used to compute the deformation gradient, the algorithm is high-order accurate and is consistent with the DG methods used to compute the fluid solution. The method is validated with a benchmark of a periodic gyre, a vortex advected in uniform flow and the flow around a square cylinder. An exact equation for the FTLE of the advected vortex is derived.

High Fidelity Spectral/hp Element Methods for Turbomachinery

2018 ◽  
Author(s):  
Andrea Cassinelli ◽  
Francesco Montomoli ◽  
Paolo Adami ◽  
Spencer J. Sherwin
Keyword(s):  
Best Practices ◽  
Computational Cost ◽  
Spectral Element ◽  
High Order ◽  
Software Framework ◽  
High Fidelity ◽  
Strong Impact ◽  
Spectral Element Methods ◽  
Base Reference ◽  
High Reynolds

The high order spectral/hp element methods implemented in the software framework Nektar++ are investigated for scale-resolving simulations of LPT profiles. There is a growing demand for high fidelity methods for turbomachinery to move towards numerical “experiments”. The study contributes at building best practices for the use of emerging high fidelity spectral element methods in turbomachinery predictions, with focus on the numerical details that are specific of these classes of methods. For this reason, the T106A cascade is used as a base reference application because of availability of data from previous investigations. The effects of polynomial order (p-refinement), spanwise domain extent and spanwise Fourier planes are considered, looking at flow statistics, convergence and sensitivity of the results. The performance of the high order spectral/hp element method is also assessed through validation against experimental data at moderately high Reynolds number. Thanks to the reduced computational cost, the proposed methods will have a strong impact in turbomachinery, paving the way to its use for design purposes and also allowing for a deeper understanding of the flow physics.

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