Alexander van Zuijlen

Fast unsteady flow computations with a Jacobian-free Newton-Krylov algorithm

Despite the advances in computer power and numerical algorithms over the last decades, solutions to unsteady flow problems remain computing time intensive. Especially for large Reynolds number flows, nonlinear multigrid, which is commonly used to solve the nonlinear systems of equations, converges slowly. The stiffness induced by the large aspect ratio cells and turbulence is not tackled well by this solution method. In previous work we showed that a Jacobian-free Newton-Krylov (jfnk) algorithm, preconditioned with an approximate factorization of the Jacobian that approximately matches the target residual operator, enables a speed up of a factor of 10 compared to standard nonlinear multigrid for two-dimensional, large Reynolds number, unsteady flow computations. The goal of this paper is to demonstrate that the jfnk algorithm is also suited to tackle the stiffness induced by the maximum aspect ratio, the grid density, the physical time step and the Reynolds number. Compared to standard nonlinear multigrid, speed ups up to a factor of 25 are achieved.

Parallel coupling numerics for partitioned fluid–structure interaction simulations

Abstract Within the last decade, very sophisticated numerical methods for the iterative and partitioned solution of fluid–structure interaction problems have been developed that allow for high accuracy and very complex scenarios. The combination of these two aspects–accuracy and complexity–demands very high computational grid resolutions and, thus, high performance computing methods designed for massively parallel hardware architectures. For those architectures, currently used coupling methods, which mainly work with a staggered execution of the fluid and the structure solver, i.e., the execution of one solver after the other in every outer iteration, lead to severe load imbalances: if the flow solver, e.g., scales on a very large number of processors but the structural solver does not due to its limited amount of data and required operations, almost all processors assigned to the coupled simulations are idle during the execution of the structure solver. We propose two new iterative coupling methods that allow for the simultaneous execution of flow and structure solvers. In both cases, we show that pure fixed-point iterations based on the parallel execution of the solvers do not lead to good results, but the combination of parallel solver execution and so-called quasi-Newton methods yields very efficient and robust methods. Those methods are known to be very efficient also for the stabilization of critical scenarios solved with the standard staggered solver execution. We demonstrate the competitive convergence of our methods for various established benchmark scenarios. Both methods are perfectly suited for use with black-box solvers because the quasi-Newton approach uses solely input and output information of the solvers to approximate the effect of the unknown Jacobians that would be required in a standard Newton solver.

Radial basis function mesh deformation including surface orthogonality

Orthogonality of a mesh is one of the mesh metrics used to determine the quality of the mesh. Generally RBF mesh deformation is good in preserving orthogonality. However, in the case of linear elastic deformations, where the displacements in different directions are independent of each other, this it not the case. We propose a solution of incorporating orthogonality explicitly in the formulation by adding additional points near the boundary. To limit the increase in computational cost (due to the increase of points), two modifications of the greedy algorithm are proposed. A 2D channel test case with a 1D linearly deforming membrane is used to test the proposed methods. From the initial results it can be concluded that the orthogonality is reduced significantly (from 31.9 to 1.3 degree) with the proposed method. Using the optimized greedy algorithm with a orthogonality driven approach, results in the lowest number selected control points for a given set of requirements (40 versus 27 for original rbf and greedy).

Effectiveness of Side Force Models for Flow Simulations Downstream of Vortex Generators

Vortex generators are a widely used means of flow control, and predictions of their influence are vital for efficient designs. However, accurate computational fluid dynamics simulations of their effect on the flowfield by means of a body-fitted mesh are computationally expensive. Therefore, the Bender–Anderson–Yagle and jBAY models, which represent the effect of vortex generators on the flow using source terms in the momentum equations, are popular in industry. In this contribution, the ability of the Bender–Anderson–Yagle and jBAY models to provide accurate flowfield results is examined by looking at boundary-layer properties close behind vortex generators. The results are compared with both body-fitted mesh and other source term model Reynolds-averaged Navier–Stokes simulations of three-dimensional incompressible flows over flat-plate and airfoil geometries. The influence of mesh resolution and the domain of application on the accuracy of the models is shown, and the influence of the source term on the ...

A comparison of Rosenbrock and ESDIRK methods combined with iterative solvers for unsteady compressible flows

In this article, we endeavour to find a fast solver for finite volume discretizations for compressible unsteady viscous flows. Thereby, we concentrate on comparing the efficiency of important classes of time integration schemes, namely time adaptive Rosenbrock, singly diagonally implicit (SDIRK) and explicit first stage singly diagonally implicit Runge-Kutta (ESDIRK) methods. To make the comparison fair, efficient equation system solvers need to be chosen and a smart choice of tolerances is needed. This is determined from the tolerance TOL that steers time adaptivity. For implicit Runge-Kutta methods, the solver is given by preconditioned inexact Jacobian-free Newton-Krylov (JFNK) and for Rosenbrock, it is preconditioned Jacobian-free GMRES. To specify the tolerances in there, we suggest a simple strategy of using TOL/100 that is a good compromise between stability and computational effort. Numerical experiments for different test cases show that the fourth order Rosenbrock method RODASP and the fourth order ESDIRK method ESDIRK4 are best for fine tolerances, with RODASP being the most robust scheme.

High Order Time Integration For Fluid-Structure Interaction on Moving Meshes

In this paper high order time integration schemes are investigated for the integration of uid-structure interaction (FSI) model problem with deforming domains. The integration algorithm consists of a partitioned scheme in which a combination of implicit and explicit (IMEX) high order Runge-Kutta time integration schemes is used: the uid and structure systems are decoupled at their interface and both systems are integrated using the implicit system under a given boundary condition at the interface. The inuence of this boundary condition (the coupling term) is integrated using the explicit Runge-Kutta scheme. The uid dynamics are written in the arbitrary Lagrange Eulerian formulation to cope with the deforming uid mesh. An expression is proposed for the mesh face velocities of the deforming mesh such that the discrete geometric conservation law is satised. For the model problem numerical investigations are made into the eciency of these high order time integration schemes compared to lower order methods. The IMEX scheme retains the order of the implicit and explicit schemes and obtains the same accuracy as a second order staggered scheme for less computational work.

Numerical simulation of transitional flow on a wind turbine airfoil with RANS-based transition model

ABSTRACT This paper presents a numerical investigation of transitional flow on the wind turbine airfoil DU91-W2-250 with chord-based Reynolds number Rec = 1.0 × 106. The Reynolds-averaged Navier–Stokes based transition model using laminar kinetic energy concept, namely the k − kL − ω model, is employed to resolve the boundary layer transition. Some ambiguities for this model are discussed and it is further implemented into OpenFOAM-2.1.1. The k − kL − ω model is first validated through the chosen wind turbine airfoil at the angle of attack (AoA) of 6.24° against wind tunnel measurement, where lift and drag coefficients, surface pressure distribution and transition location are compared. In order to reveal the transitional flow on the airfoil, the mean boundary layer profiles in three zones, namely the laminar, transitional and fully turbulent regimes, are investigated. Observation of flow at the transition location identifies the laminar separation bubble. The AoA effect on boundary layer transition over wind turbine airfoil is also studied. Increasing the AoA from −3° to 10°, the laminar separation bubble moves upstream and reduces in size, which is in close agreement with wind tunnel measurement.

Energy-conserving schemes for wind farm aerodynamics

Computational demands compel researchers to use coarse grids for the study of wind farm aerodynamics, which necessitates the use of accurate numerical schemes. Energy- conserving (EC) schemes are designed to enforce the conservation of Kinetic Energy (KE), an invariant property of incompressible flows. These schemes are numerically stable and free from artificial dissipation, even on coarse grids and could be used as an alternative to high-order pseudo-spectral schemes. This article details tests on EC schemes in the context of Large Eddy Simulations (LES). Results suggest that the accuracy of EC schemes is influenced by the Subgrid Scale model used for the LES. EC methods use central schemes that lead to dispersion, which is more apparent with a less-dissipative Scale Similarity model. Whereas, the purely dissipative Smagorinskys model reduces the dispersion and generates a smoother solution but at the cost of accuracy in terms of predicting the KE. Although the impact of EC schemes and SGS models on the LES of wind farms is yet to be assessed, a simple LES of a model wind farm uncovers that EC schemes are quite suitable for wind farm aerodynamics.

Implicit and Explicit Higher Order Time Integration Schemes for Fluid-Structure Interaction Computations

In this paper higher order time integration schemes are applied to fluid-structure interaction (FSI) simulations. For a given accuracy, we investigate the efficiency of higher order time integration schemes compared to lower order methods. In the partitioned FSI simulations on a one-dimensional piston problem, a mixed implicit/explicit (IMEX) time integration scheme is employed: the implicit scheme is used to integrate the fluid and structural dynamics, whereas an explicit Runge-Kutta scheme integrates the coupling terms. The resulting IMEX scheme retains the order of the implicit and explicit schemes. In the IMEX scheme considered, the implicit scheme consists of an explicit first stage, singly diagonally implicit Runge-Kutta (ESDIRK) scheme, which is a multi-stage, L-stable scheme.

Partitioned Fluid–Structure–Acoustics Interaction on Distributed Data: Numerical Results and Visualization

We present a coupled simulation approach for fluid–structure–acoustic interactions (FSAI) as an example for strongly surface coupled multi-physics problems. In addition to the multi-physics character, FSAI feature multi-scale properties as a further challenge. In our partitioned approach, the problem is split into spatially separated subdomains interacting via coupling surfaces. Within each subdomain, scalable, single-physics solvers are used to solve the respective equation systems. The surface coupling between them is realized with the scalable open-source coupling tool preCICE described in the “Partitioned Fluid–Structure–Acoustics Interaction on Distributed Data: Coupling via preCICE”. We show how this approach enables the use of existing solvers and present the overall scaling behavior for a three-dimensional test case with a bending tower generating acoustic waves. We run this simulation with different solvers demonstrating the performance of various solvers and the flexibility of the partitioned approach with the coupling tool preCICE. An efficient and scalable in-situ visualization reducing the amount of data in place at the simulation processors before sending them over the network or to a file system completes the simulation environment.