Unstructured-grid methods development for unsteady aerodynamic and aeroelastic analyses

The current status of unstructured grid methods development in the Unsteady Aerodynamics Branch at NASA-Langley is described. These methods are being developed for unsteady aerodynamic and aeroelastic analyses. The flow solvers are highlighted which were developed for the solution of the unsteady Euler equations and selected results are given which show various features of the capability. The results demonstrate 2-D and 3-D applications for both steady and unsteady flows. Comparisons are also made with solutions obtained using a structured grid code and with experimental data to determine the accuracy of the unstructured grid methodology. These comparisons show good agreement which thus verifies the accuracy

Implicit High-Order Flux Reconstruction Solver for High-Speed Compressible Flows

The present paper addresses the development and implementation of the first high-order Flux Reconstruction (FR) solver for high-speed flows within the open-source COOLFluiD (Computational Object-Oriented Libraries for Fluid Dynamics) platform. The resulting solver is fully implicit and able to simulate compressible flow problems governed by either the Euler or the Navier-Stokes equations in two and three dimensions. Furthermore, it can run in parallel on multiple CPU-cores and is designed to handle unstructured grids consisting of both straight and curved edged quadrilateral or hexahedral elements. While most of the implementation relies on state-of-the-art FR algorithms, an improved and more case-independent shock capturing scheme has been developed in order to tackle the first viscous hypersonic simulations using the FR method. Extensive verification of the FR solver has been performed through the use of reproducible benchmark test cases with flow speeds ranging from subsonic to hypersonic, up to Mach 17.6. The obtained results have been favorably compared to those available in literature. Furthermore, so-called super-accuracy is retrieved for certain cases when solving the Euler equations. The strengths of the FR solver in terms of computational accuracy per degree of freedom are also illustrated. Finally, the influence of the characterizing parameters of the FR method as well as the the influence of the novel shock capturing scheme on the accuracy of the developed solver is discussed

Simulation of flows with violent free surface motion and moving objects using unstructured grids

This is the peer reviewed version of the following article: [Löhner, R. , Yang, C. and Oñate, E. (2007), Simulation of flows with violent free surface motion and moving objects using unstructured grids. Int. J. Numer. Meth. Fluids, 53: 1315-1338. doi:10.1002/fld.1244], which has been published in final form at https://doi.org/10.1002/fld.1244. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.A volume of fluid (VOF) technique has been developed and coupled with an incompressible Euler/Navier–Stokes solver operating on adaptive, unstructured grids to simulate the interactions of extreme waves and three-dimensional structures. The present implementation follows the classic VOF implementation for the liquid–gas system, considering only the liquid phase. Extrapolation algorithms are used to obtain velocities and pressure in the gas region near the free surface. The VOF technique is validated against the classic dam-break problem, as well as series of 2D sloshing experiments and results from SPH calculations. These and a series of other examples demonstrate that the ability of the present approach to simulate violent free surface flows with strong nonlinear behaviour.Peer ReviewedPostprint (author's final draft

High Order Cell-Centered Lagrangian-Type Finite Volume Schemes with Time-Accurate Local Time Stepping on Unstructured Triangular Meshes

We present a novel cell-centered direct Arbitrary-Lagrangian-Eulerian (ALE) finite volume scheme on unstructured triangular meshes that is high order accurate in space and time and that also allows for time-accurate local time stepping (LTS). The new scheme uses the following basic ingredients: a high order WENO reconstruction in space on unstructured meshes, an element-local high-order accurate space-time Galerkin predictor that performs the time evolution of the reconstructed polynomials within each element, the computation of numerical ALE fluxes at the moving element interfaces through approximate Riemann solvers, and a one-step finite volume scheme for the time update which is directly based on the integral form of the conservation equations in space-time. The inclusion of the LTS algorithm requires a number of crucial extensions, such as a proper scheduling criterion for the time update of each element and for each node; a virtual projection of the elements contained in the reconstruction stencils of the element that has to perform the WENO reconstruction; and the proper computation of the fluxes through the space-time boundary surfaces that will inevitably contain hanging nodes in time due to the LTS algorithm. We have validated our new unstructured Lagrangian LTS approach over a wide sample of test cases solving the Euler equations of compressible gasdynamics in two space dimensions, including shock tube problems, cylindrical explosion problems, as well as specific tests typically adopted in Lagrangian calculations, such as the Kidder and the Saltzman problem. When compared to the traditional global time stepping (GTS) method, the newly proposed LTS algorithm allows to reduce the number of element updates in a given simulation by a factor that may depend on the complexity of the dynamics, but which can be as large as 4.7.Comment: 31 pages, 13 figure

Diagnostic tools for 3D unstructured oceanographic data

Most ocean models in current use are built upon structured meshes. It follows that most existing tools for extracting diagnostic quantities (volume and surface integrals, for example) from ocean model output are constructed using techniques and software tools which assume structured meshes. The greater complexity inherent in unstructured meshes (especially fully unstructured grids which are unstructured in the vertical as well as the horizontal direction) has left some oceanographers, accustomed to traditional methods, unclear on how to calculate diagnostics on these meshes. In this paper we show that tools for extracting diagnostic data from the new generation of unstructured ocean models can be constructed with relative ease using open source software. Higher level languages such as Python, in conjunction with packages such as NumPy, SciPy, VTK and MayaVi, provide many of the high-level primitives needed to perform 3D visualisation and evaluate diagnostic quantities, e.g. density fluxes. We demonstrate this in the particular case of calculating flux of vector fields through isosurfaces, using flow data obtained from the unstructured mesh finite element ocean code ICOM, however this tool can be applied to model output from any unstructured grid ocean code

Addressing the challenges of implementation of high-order finite volume schemes for atmospheric dynamics of unstructured meshes

The solution of the non-hydrostatic compressible Euler equations using Weighted Essentially Non-Oscillatory (WENO) schemes in two and three-dimensional unstructured meshes, is presented. Their key characteristics are their simplicity; accuracy; robustness; non-oscillatory properties; versatility in handling any type of grid topology; computational and parallel efficiency. Their defining characteristic is a non-linear combination of a series of high-order reconstruction polynomials arising from a series of reconstruction stencils. In the present study an explicit TVD Runge-Kutta 3rd -order method is employed due to its lower computational resources requirement compared to implicit type time advancement methods. The WENO schemes (up to 5th -order) are applied to the two dimensional and three dimensional test cases: a 2D rising

Developments and trends in three-dimensional mesh generation

An intense research effort over the last few years has produced several competing and apparently diverse methods for generating meshes. Recent progress is reviewed and the central themes are emphasized which form a solid foundation for future developments in mesh generation