Validation of a High-Order Large-Eddy Simulation Solver Using a Vertical-Axis Wind Turbine

Kanner, Samuel; Persson, Per‐Olof

doi:10.2514/1.j054138

Cited by 11 publications

(8 citation statements)

References 40 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…where γ is the adiabatic gas constant. For the viscous problems, we introduce an isentropic assumption of the form p = Kρ γ , for a given constant K, as described in [17]. This additional simplification can be thought of as an artificial compressibility model for the incompressible flows simulated in Sections 5.2 and 5.3.…”

Section: Equations and Spatial Discretizationmentioning

confidence: 99%

See 1 more Smart Citation

Stage-parallel fully implicit Runge–Kutta solvers for discontinuous Galerkin fluid simulations

Pazner¹,

Persson²

2017

Journal of Computational Physics

Self Cite

View full text Add to dashboard Cite

In this paper, we develop new techniques for solving the large, coupled linear systems that arise from fully implicit Runge-Kutta methods. This method makes use of the iterative preconditioned GMRES algorithm for solving the linear systems, which has seen success for fluid flow problems and discontinuous Galerkin discretizations. By transforming the resulting linear system of equations, one can obtain a method which is much less computationally expensive than the untransformed formulation, and which compares competitively with other time-integration schemes, such as diagonally implicit Runge-Kutta (DIRK) methods. We develop and test several ILU-based preconditioners effective for these large systems. We additionally employ a parallel-in-time strategy to compute the Runge-Kutta stages simultaneously. Numerical experiments are performed on the Navier-Stokes equations using Euler vortex and 2D and 3D NACA airfoil test cases in serial and in parallel settings. The fully implicit Radau IIA Runge-Kutta methods compare favorably with equal-order DIRK methods in terms of accuracy, number of GMRES iterations, number of matrix-vector multiplications, and wall-clock time, for a wide range of time steps.

show abstract

Section: Equations and Spatial Discretizationmentioning

confidence: 99%

“…Within each group, each process is then assigned to one stage of the IRK method. Thus, when assembling the block matrix of the form (17), the Jacobian matrices for all of the stages are computed in parallel. This does not require any communication between the groups.…”

Section: Stage-parallelism and Partitioned Ilumentioning

confidence: 99%

Stage-parallel fully implicit Runge–Kutta solvers for discontinuous Galerkin fluid simulations

Pazner¹,

Persson²

2017

Journal of Computational Physics

Self Cite

View full text Add to dashboard Cite

show abstract

“…The determination of the actual α 0 used in the experiments is discussed in Ref. 12. We chose the static 'toe-out' angle of each of the airfoils α 0 to be 2 • , since it best matches the experimental data.…”

Section: Iib Model Turbinementioning

confidence: 99%

“…However, since the turbines rotate individually around their center axes, we cannot simply rotate the entire mesh like was done in the single turbine case in Ref. 12. Instead, we use the following moving-mesh strategy that incorporates rigid rotations that stretch the elements as well as techniques to change the element connectivities to prevent poor element qualities.…”

Section: Iiia Computational Domain and Moving Mesh Strategymentioning

confidence: 99%

Implicit Large-Eddy Simulation of 2D Counter-Rotating Vertical-Axis Wind Turbines

Kanner

Wang

Persson

2016

34th Wind Energy Symposium

Self Cite

View full text Add to dashboard Cite

Recent theoretical and experimental work has suggested that placing a vertical-axis wind turbine near a similar turbine that is rotating in the opposite direction may improve the efficiency of both turbines. A high-order Implicit Large Eddy Simulations (ILES) method is used to confirm these results by modeling a 2D cross-section of the wind turbines. In order to account for the moving domain, an element flipping technique is employed. This approach flips elements and uses an L 2-projection on the interfaces between the rotating turbines and the static outer mesh region. An Arbitrary-Lagrangian-Eulerian method is used to solve for the dynamic pressure and shear stress on the turbine blades using an isentropic formulation of the compressible Navier-Stokes equation. Our preliminary results seem to confirm those of the recently published experiments for straight-bladed, counterrotating turbines. When the turbines are oriented such that a line connecting their centers of rotation is perpendicular to the incident wind direction, the power coefficient of each turbine can increase by more than 10%. In fact, when the turbines are oriented in a doublet-like configuration, where the blades travel upwind in the interior region between the turbines, our simulations show that the power coefficient of each turbine is increased by 15%. However, unlike the experimental results, when the incident wind is oriented parallel to this line, the power coefficient of the shadowed turbine is reduced significantly. We show snapshots of the fluid velocity and hypothesize why the power of the turbines may be increased due to blockage effects. That is, at certain azimuthal angles the relative wind speed that the blade encounters is larger than in the isolated case.

show abstract

“…Using eigenvalue analyses, it is possible to derive tight upper bounds on the condition number of (19) for all γ ∈ (0, ∞) when L is symmetric negative semi-definite (SNSD) or skew symmetric (SS) (see [4] for related derivations). These tight upper bounds achieve equality for all γ ∈ (0, ∞) as the spectrum of L becomes dense in [0, ∞) for SNSD L, and dense in (−i∞, i∞) for SS L. In each case, the tight upper bounds are minimized over all γ ∈ (0, ∞) when γ = γ * , for γ * given by (23), which is perhaps unsurprising given Corollary 1. At the minimum γ = γ * , the tight bound for the SNSD case is…”

mentioning

confidence: 91%

Fast solution of fully implicit Runge-Kutta and discontinuous Galerkin in time for numerical PDEs, Part II: nonlinearities and DAEs

Southworth¹,

Krzysik²,

Pazner³

2021

Preprint

View full text Add to dashboard Cite

Fully implicit Runge-Kutta (IRK) methods have many desirable accuracy and stability properties as time integration schemes, but are rarely used in practice with large-scale numerical PDEs because of the difficulty of solving the stage equations. This paper introduces a theoretical and algorithmic framework for the fast, parallel solution of the nonlinear equations that arise from IRK methods applied to nonlinear numerical PDEs, including PDEs with algebraic constraints. This framework also naturally applies to discontinuous Galerkin discretizations in time. Moreover, the new method is built using the same preconditioners needed for backward Euler-type time stepping schemes. Several new linearizations of the nonlinear IRK equations are developed, offering faster and more robust convergence than the often-considered simplified Newton, as well as an effective preconditioner for the true Jacobian if exact Newton iterations are desired. Inverting these linearizations requires solving a set of block 2 × 2 systems. Under quite general assumptions on the spatial discretization, it is proven that the preconditioned operator has a condition number of ∼ O(1), with only weak dependence on the number of stages or integration accuracy. The new methods are applied to several challenging fluid flow problems, including the compressible Euler and Navier Stokes equations, and the vorticity-streamfunction formulation of the incompressible Euler and Navier Stokes equations. Up to 10th-order accuracy is demonstrated using Gauss integration, while in all cases 4th-order Gauss integration requires roughly half the number of preconditioner applications as required by standard SDIRK methods.

show abstract

Validation of a High-Order Large-Eddy Simulation Solver Using a Vertical-Axis Wind Turbine

Cited by 11 publications

References 40 publications

Stage-parallel fully implicit Runge–Kutta solvers for discontinuous Galerkin fluid simulations

Stage-parallel fully implicit Runge–Kutta solvers for discontinuous Galerkin fluid simulations

Implicit Large-Eddy Simulation of 2D Counter-Rotating Vertical-Axis Wind Turbines

Fast solution of fully implicit Runge-Kutta and discontinuous Galerkin in time for numerical PDEs, Part II: nonlinearities and DAEs

Contact Info

Product

Resources

About