Rainald Löhner

An adaptive finite element scheme for transient problems in CFD

Abstract An adaptive finite element scheme for transient problems is presented. The classic h -enrichment / coarsening is employed in conjunction with a triangular finite element discretization in two dimensions. A mesh change is performed every n timesteps, depending on the Courant number employed and the number of ‘protective layers’ added ahead of the refined region. In order to simplify the refinement/ coarsening logic and to be as fast as possible, only one level of refinement/coarsening is allowed per mesh change. A high degree of vectorizability has been achieved on the CRAY XMP 12 at NRL. Several examples involving shock-shock interactions and the impact of shocks on structures demonstrate the performance of the method, indicating that considerable savings in CPU time and storage can be realized even for strongly unsteady flows.

Improved ALE mesh velocities for moving bodies

A Laplacian smoothing of the mesh velocities with variable diffusivity based on the distance from moving bodies is introduced. This variable diffusivity enforces a more uniform mesh velocity in the region close to the moving bodies. Given that in most applications these are regions where small elements are located, the new procedure decreases element distortion considerably, reducing the need for local or global remeshing, and in some cases avoiding it altogether.

A Hermite WENO-based limiter for discontinuous Galerkin method on unstructured grids

A weighted essentially non-oscillatory reconstruction scheme based on Hermite polynomials is developed and applied as a limiter for the discontinuous Galerkin finite element method on unstructured grids. The solution polynomials are reconstructed using a WENO scheme by taking advantage of handily available and yet valuable information, namely the derivatives, in the context of the discontinuous Galerkin method. The stencils used in the reconstruction involve only the van Neumann neighborhood and are compact and consistent with the DG method. The developed HWENO limiter is implemented and used in a discontinuous Galerkin method to compute a variety of both steady-state and time-accurate compressible flow problems on unstructured grids. Numerical experiments for a wide range of flow conditions in both 2D and 3D configurations are presented to demonstrate the accuracy, effectiveness, and robustness of the designed HWENO limiter for the DG methods.

A discontinuous Galerkin method based on a Taylor basis for the compressible flows on arbitrary grids

A discontinuous Galerkin method based on a Taylor basis is presented for the solution of the compressible Euler equations on arbitrary grids. Unlike the traditional discontinuous Galerkin methods, where either standard Lagrange finite element or hierarchical node-based basis functions are used to represent numerical polynomial solutions in each element, this DG method represents the numerical polynomial solutions using a Taylor series expansion at the centroid of the cell. Consequently, this formulation is able to provide a unified framework, where both cell-centered and vertex-centered finite volume schemes can be viewed as special cases of this discontinuous Galerkin method by choosing reconstruction schemes to compute the derivatives, offer the insight why the DG methods are a better approach than the finite volume methods based on either TVD/MUSCL reconstruction or essentially non-oscillatory (ENO)/weighted essentially non-oscillatory (WENO) reconstruction, and has a number of distinct, desirable, and attractive features, which can be effectively used to address some of shortcomings of the DG methods. The developed method is used to compute a variety of both steady-state and time-accurate flow problems on arbitrary grids. The numerical results demonstrated the superior accuracy of this discontinuous Galerkin method in comparison with a second order finite volume method and a third-order WENO method, indicating its promise and potential to become not just a competitive but simply a superior approach than its finite volume and ENO/WENO counterparts for solving flow problems of scientific and industrial interest.

Conservative Load Projection and Tracking for Fluid-Structure Problems

The loose coupling of computational fluid dynamics and computational structural dynamics solvers introduces some problems related to the information transfer between the codes. Some techniques developed to solve the problems of the load transfer and interface surface tracking are presented. The main criterion is to achieve conservation of total loads and total energy. The load projection scheme is based on Gaussian integration and fast interpolation algorithms for unstructured grids. The surface tracking algorithm, also based on interpolation, is important for many applications, including aeroelastic deformation of wings due to aerodynamic loads. The methodologies not only improve present fluid-structure interaction simulations, but also increase the range of their applicability. These techniques are of general character and can be used in other multidisciplinary applications as well.

Adaptive remeshing for transient problems

Abstract Adaptive remeshing schemes for transient problems are presented. The main advantage of these schemes is the ease in incorporating directional refinement and body motion in the context of adaptive refinement. Practical numerical examples for the Euler equations, run on the CRAY-XMP-24 at NRL, show that the adaptive remeshing scheme by itself cannot compete with ordinary h-refinement for strongly unsteady flows that require a grid change every 5–10 timesteps. Therefore, we study the combination of adaptive remeshing and h-refinement. After generating a coarser grid with stretched elements, the whole grid is h-refined at once. Even with one level of h-refinement, the combined scheme easily out-performs ordinary h-refinement, yielding a very effective adaptive refinement method for this class of problems.

Edge-based finite element scheme for the Euler equations

We describe the development, validation, and application of a new finite element scheme for the solution of the compressible Euler equations on unstructured grids. The implementation of the numerical scheme is based on an edge-based data structure, as opposed to a more traditional element-based data structure. The use of this edge-based data structure not only improves the efficiency of the algorithm but also enables a straightforward implementation of upwind schemes in the context of finite element methods. The algorithm has been tested and validated on some well-documented configurations. A flow solution about a complete F-18 fighter is shown to demonstrate the accuracy and robustness of the proposed algorithm

Automatic unstructured grid generators

Abstract A review of automatic unstructured grid generators is given. These types of grids have found widespread use in computational fluid dynamics, computational structural dynamics, computational electro-magnetics and computational thermodynamics. The following topics are treated: the methods most commonly used, the specification of desired element size/shape and surface definition/meshing. Finally, the use of automatic grid generators as an enabling technology for moving body simulations and adaptive remeshing techniques is discussed.

Efficient simulation of blood flow past complex endovascular devices using an adaptive embedding technique

The simulation of blood flow past endovascular devices such as coils and stents is a challenging problem due to the complex geometry of the devices. Traditional unstructured grid computational fluid dynamics relies on the generation of finite element grids that conform to the boundary of the computational domain. However, the generation of such grids for patient-specific modeling of cerebral aneurysm treatment with coils or stents is extremely difficult and time consuming. This paper describes the application of an adaptive grid embedding technique previously developed for complex fluid structure interaction problems to the simulation of endovascular devices. A hybrid approach is used: the vessel walls are treated with body conforming grids and the endovascular devices with an adaptive mesh embedding technique. This methodology fits naturally in the framework of image-based computational fluid dynamics and opens the door for exploration of different therapeutic options and personalization of endovascular procedures.

Comparisons of model simulations with observations of mean flow and turbulence within simple obstacle arrays

Abstract A three-dimensional numerical code with unstructured tetrahedral grids, the finite element flow solver (FEFLO), was used to simulate the mean flow and the turbulence within obstacle array configurations consisting of simple cubical elements. Model simulations were compared with observations from a hydraulic water flume at the University of Waterloo. FEFLO was run in large eddy simulation mode, using the Smagorinsky closure model, to resolve the larger scales of the flow field. There were four experiment test cases consisting of square and staggered arrays of cubical obstacles with separations of 1.5 and 0.5 obstacle heights. The mean velocity profile for the incoming neutral boundary layer was approximated by a power law, and the turbulent fluctuations in the approach flow were generated using a Monte Carlo model. The numerical simulations were able to capture, within 40% on average, the general characteristics of the mean flow and the turbulence, such as the strong mean wind shears and the maximum turbulence at the elevation of the obstacles and the nearly constant mean wind and the 50% reduction in the turbulent velocity within the obstacle canopy. As expected, the mean wind speeds were significantly decreased (by about a factor of two or three) in the array with closer obstacle packing. It was found that, a “street canyon” effect was more obvious for the square arrays, with higher flow speeds in between the obstacles, than for the staggered arrays.