D.S. Blom

Adaptive radial basis function mesh deformation using data reduction

Radial Basis Function (RBF) mesh deformation is one of the most robust mesh deformation methods available. Using the greedy (data reduction) method in combination with an explicit boundary correction, results in an efficient method as shown in literature. However, to ensure the method remains robust, two issues are addressed: 1) how to ensure that the set of control points remains an accurate representation of the geometry in time and 2) how to use/automate the explicit boundary correction, while ensuring a high mesh quality. In this paper, we propose an adaptive RBF mesh deformation method, which ensures the set of control points always represents the geometry/displacement up to a certain (user-specified) criteria, by keeping track of the boundary error throughout the simulation and re-selecting when needed. Opposed to the unit displacement and prescribed displacement selection methods, the adaptive method is more robust, user-independent and efficient, for the cases considered. Secondly, the analysis of a single high aspect ratio cell is used to formulate an equation for the correction radius needed, depending on the characteristics of the correction function used, maximum aspect ratio, minimum first cell height and boundary error. Based on the analysis two new radial basis correction functions are derived and proposed. This proposed automated procedure is verified while varying the correction function, Reynolds number (and thus first cell height and aspect ratio) and boundary error. Finally, the parallel efficiency is studied for the two adaptive methods, unit displacement and prescribed displacement for both the CPU as well as the memory formulation with a 2D oscillating and translating airfoil with oscillating flap, a 3D flexible locally deforming tube and deforming wind turbine blade. Generally, the memory formulation requires less work (due to the large amount of work required for evaluating RBFs), but the parallel efficiency reduces due to the limited bandwidth available between CPU and memory. In terms of parallel efficiency/scaling the different studied methods perform similarly, with the greedy algorithm being the bottleneck. In terms of absolute computational work the adaptive methods are better for the cases studied due to their more efficient selection of the control points. By automating most of the RBF mesh deformation, a robust, efficient and almost user-independent mesh deformation method is presented.

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.

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.

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.

A Review on Fast Quasi-Newton and Accelerated Fixed-Point Iterations for Partitioned Fluid–Structure Interaction Simulation

The partitioned simulation of fluid–structure interactions offers great flexibility in terms of exchanging flow and structure solver and using existing established codes. However, it often suffers from slow convergence and limited parallel scalability. Quasi-Newton or accelerated fixed-point iterations are a very efficient way to solve the convergence issue. At the same time, they stabilize and speed up not only the standard staggered fluid–structure coupling iterations, but also the variant with simultaneous execution of flow and structure solver that is fairly inefficient if no acceleration methods for the underlying fixed-point iteration are used. In this chapter, we present a review on combinations of iteration patterns (parallel and staggered) and of quasi-Newton methods and compare their suitability in terms of convergence speed, robustness, and parallel scalability. Some of these variants use the so-called manifold mapping that yields an additional speedup by using an approach that can be interpreted as a generalization of the multi-level idea.

Multi-Level Acceleration of Parallel Coupled Partitioned Fluid-Structure Interaction with Manifold Mapping

Strongly coupled fluid-structure interaction simulations often suffer from slow convergence, limited parallel scalability or difficulties in using black-box solvers. As partitioned simulations still play an important role in cases where new combinations of models, discretizations and codes have to be tested in an easy and fast way, we propose a combination of a parallel black-box coupling with a manifold mapping algorithm as an acceleration method. In this approach, we combine a computationally inexpensive low-fidelity FSI model with a high-fidelity FSI model to reduce the number of coupling iterations of the high fidelity FSI model. Information from previous time steps is taken into account with a secant update step similar to the Broyden update. The used black-box approach is applied for an incompressible laminar flow over a fixed cylinder with an attached flexible flap and a wave propagation in a three-dimensional elastic tube problem. A reduction of approximately 55 % in terms of high fidelity iterations is achieved compared to the Anderson mixing method if the fluid and the structure solvers are executed in parallel.