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.

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

A Novel Variant of the K-ω URANS Model for Spectral Element Methods: Implementation, Verification, and Validation in Nek5000

2014 ◽  
Author(s):  
A. Tomboulides ◽  
S. M. Aithal ◽  
P. F. Fischer ◽  
E. Merzari ◽  
A. Obabko
Keyword(s):  
Ad Hoc ◽  
Computational Cost ◽  
Detailed Comparison ◽  
Spectral Element ◽  
Navier Stokes ◽  
Present Formulation ◽  
Spectral Element Methods ◽  
Novel Variants ◽  
Sst Model ◽  
Novel Variant

Unsteady Reynolds-averaged Navier-Stokes (uRANS) models can provide good engineering estimates of wall shear and heat flux at a significantly lower computational cost compared with LES simulations. In this paper, we discuss the implementation of two novel variants of the k-ω turbulence model, the regularized k-ω standard and the regularized k-ω SST model, in a spectral element code, Nek5000. We present formulation for the specific dissipation rate (ω) in the standard k-ω model, which would obviate the need for ad hoc boundary conditions of ω on the wall. The regularized approach is designed to lead to grid-independent solutions as resolution is increased. We present a detailed comparison of these novel methods for various standard problems including the T-junction benchmark problem. The two approaches presented in this work compare very well with the standard k-ω model and experimental data for all the cases studied.

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-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 Vertical Discretization for a Nonhydrostatic Atmospheric Model Based on High-Order Spectral Elements

2019 ◽  
Vol 148 (1) ◽  
pp. 415-436
Author(s):  
Tae-Hyeong Yi ◽  
Francis X. Giraldo
Keyword(s):  
Computational Cost ◽  
Element Model ◽  
Atmospheric Model ◽  
Spectral Element ◽  
High Order ◽  
Spectral Elements ◽  
Test Cases ◽  
Governing Equations ◽  
Discretization Methods ◽  
Element Approach

Abstract This study addresses the treatment of vertical discretization for a high-order, spectral element model of a nonhydrostatic atmosphere in which the governing equations of the model are separated into horizontal and vertical components by introducing a coordinate transformation, so that one can use different orders and types of approximations in both directions. The vertical terms of the decoupled governing equations are discretized using finite elements based on either Lagrange or basis-spline polynomial functions in the sigma coordinate, while maintaining the high-order spectral elements for the discretization of the horizontal terms. This leads to the fact that the high-order model of spectral elements with a nonuniform grid, interpolated within an element, can be easily accommodated with existing physical parameterizations. Idealized tests are performed to compare the accuracy and efficiency of the vertical discretization methods, in addition to the central finite differences, with those of the standard high-order spectral element approach. Our results show, through all the test cases, that the finite element with the cubic basis-spline function is more accurate than the other vertical discretization methods at moderate computational cost. Furthermore, grid dependency studies in the tests with and without orography indicate that the convergence rate of the vertical discretization methods is lower than the expected level of discretization accuracy, especially in the Schär mountain test, which yields approximately first-order convergence.

scholarly journals Dealiasing techniques for high-order spectral element methods on regular and irregular grids

2015 ◽  
Vol 299 ◽  
pp. 56-81 ◽  
Author(s):  
G. Mengaldo ◽  
D. De Grazia ◽  
D. Moxey ◽  
P.E. Vincent ◽  
S.J. Sherwin
Keyword(s):  
Spectral Element ◽  
High Order ◽  
Spectral Element Methods ◽  
Irregular Grids
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