We describe the implementation of a computational fluid dynamics solver for the simulation of high-speed flows. It comprises a finite volume (FV) discretization using semi-discrete, non-staggered central schemes for colocated variables prescribed on a mesh of polyhedral cells that have an arbitrary number of faces. We describe the solver in detail, explaining the choice of variables whose face interpolation is limited, the choice of limiter, and a method for limiting the interpolation of a vector field that is independent of the coordinate system. The solution of momentum and energy transport in the Navier Stokes equations uses an operator-splitting approach: first, we solve an explicit predictor equation for the convection of conserved variables, then an implicit corrector equation for the diffusion of primitive variables. Our solver is validated against four sets of data: (1) an analytical solution of the one-dimensional shock tube case; (2) a numerical solution of two dimensional, transient, supersonic flow over a forward-facing step; (3) interferogram density measurements of a supersonic jet from a circular nozzle; and (4) pressure and heat transfer measurements in hypersonic flow over a 25 degrees-55 degrees biconic. Our results indicate that the central-upwind scheme of Kurganov, Noelle and Petrova (SIAM J. Sci. Comput. 2001; 23:707-740) is competitive with the best methods previously published (e.g. piecewise parabolic method, Roe solver with van Leer limiting) and that it is inherently simple and well suited to a colocated, polyhedral FV framework. Copyright 2009 John Wiley & Sons, Ltd.
Benchmark configurations for quantitative validation and comparison of incompressible interfacial flow codes, which model two-dimensional bubbles rising in liquid columns, are proposed. The benchmark quantities: circularity, center of mass, and mean rise velocity are defined and measured to monitor convergence toward a reference solution. Comprehensive studies are undertaken by three independent research groups, two representing Eulerian level set finite-element codes and one representing an arbitrary Lagrangian-Eulerian moving grid approach. The first benchmark test case considers a bubble with small density and viscosity ratios, which undergoes moderate shape deformation. The results from all codes agree very well allowing for target reference values to be established. For the second test case, a bubble with a very low density compared to that of the Surrounding fluid, the results for all groups are in good agreement Lip to the point of break Lip, after which all three codes predict different bubble shapes. This highlights the need for the research community to invest more effort in obtaining reference solutions to problems involving break LIP and coalescence. Other research groups are encouraged to participate in these benchmarks by contacting the authors and submitting their own data. The reference data for the computed benchmark quantities can also be Supplied for validation purposes. Copyright (C) 2008 John Wiley & Sons, Ltd.
This paper describes the formulation, verification, and validation of a depth-integrated, non-hydrostatic model with a semi-implicit, finite difference scheme. The Formulation builds on the nonlinear shallow-water equations and utilizes a non-hydrostatic pressure term to describe weakly dispersive waves. A momentum-conserved advection scheme enables modeling of breaking waves without the aid of analytical solutions for bore approximation or empirical equations for energy dissipation. An upwind scheme extrapolates the free-surface elevation instead of the flow depth to provide the flux in the momentum and continuity equations. This greatly improves the model stability, which is essential for computation of energetic breaking waves and run-up. The computed results show very good agreement with laboratory data for wave propagation, transformation, breaking, and run-up. Since the numerical scheme to the momentum and continuity equations remains explicit, the implicit non-hydrostatic solution is directly applicable to existing nonlinear shallow-water models. Copyright (C) 2008 John Wiley & Sons, Ltd.
In this paper, we investigate the accuracy and efficiency of discontinuous Galerkin spectral method simulations of under-resolved transitional and turbulent flows at moderate Reynolds numbers, where the accurate prediction of closely coupled laminar regions, transition and developed turbulence presents a great challenge to large eddy simulation modelling. We take full advantage of the low numerical errors and associated superior scale resolving capabilities of high-order spectral methods by using high-order ansatz functions up to 12th order. We employ polynomial de-aliasing techniques to prevent instabilities arising from inexact quadrature of nonlinearities. Without the need for any additional filtering, explicit or implicit modelling, or artificial dissipation, our high-order schemes capture the turbulent flow at the considered Reynolds number range very well. Three classical large eddy simulation benchmark problems are considered: a circular cylinder flow at Re-D=3900, a confined periodic hill flow at Re-h=2800 and the transitional flow over a SD7003 airfoil at Re-c=60,000. For all computations, the total number of degrees of freedom used for the discontinuous Galerkin spectral method simulations is chosen to be equal or considerably less than the reported data in literature. In all three cases, we achieve an equal or better match to direct numerical simulation results, compared with other schemes of lower order with explicitly or implicitly added subgrid scale models. Copyright (c) 2014 John Wiley & Sons, Ltd.
The space-time fluid-structure interaction (FSI) techniques developed by the Team for Advanced Flow Simulation and Modeling (T*AFSM) have been applied to a wide range of 3D computation of FSI problems. some as early as in 1994 and many with challenging complexities. In this paper, we review these space-time FSI techniques and describe the enhancements introduced recently by the T*AFSM to increase the scope. accuracy, robustness and efficiency of these techniques. The aspects of the FSI solution process enhanced include the deforming-spatial-domain/stabilized space-time (DSD/SST) formulation, the fluid-structure interface conditions, the preconditioning techniques used in iterative solution of the linear equation systems, and a contact algorithm protecting the quality of the fluid mechanics mesh between the structural surfaces coming into contact. We present a number of 3D numerical examples computed with these new stabilized space-time FSI (SSTFSI) techniques. Copyright (c) 2007 John Wiley & Sons, Ltd.
A computational study of a high‐fidelity, implicit large‐eddy simulation (ILES) technique with and without the use of the dynamic Smagorinsky subgrid‐scale (SGS) model is conducted to examine the contributions of the SGS model on solutions of transitional flow over the SD7003 airfoil section. ILES without an SGS model has been shown in the past to produce comparable and sometimes favorable results to traditional SGS‐based large‐eddy simulation (LES) when applied to canonical turbulent flows. This paper evaluates the necessity of the SGS model for low‐Reynolds number airfoil applications to affirm the use of ILES without SGS‐modeling for a broader class of problems such as those pertaining to micro air vehicles and low‐pressure turbines. It is determined that the addition of the dynamic Smagorinsky model does not significantly affect the time‐mean flow or statistical quantities measured around the airfoil section for the spatial resolutions and Reynolds numbers examined in this study. Additionally, the robustness and reduced computational cost of ILES without the SGS model demonstrates the attractiveness of ILES as an alternative to traditional LES. Published 2012. This article is a US Government work and is in the public domain in the USA. The conclusions of this work affirm the application of high fidelity, implicit large‐eddy simulation without subgrid‐scale modeling to a broader class of low‐Reynolds number, transitional and turbulent flows such as those encountered by micro‐air vehicles or low‐pressure turbine blades.
New special fluid-structure interaction (FSI) techniques, supplementing the ones developed earlier, are employed with the Stabilized Space-Time FSI (SSTFSI) technique. The new special techniques include improved ways of calculating the equivalent fabric porosity in Homogenized Modeling of Geometric Porosity (HMGP), improved ways of building a starting point in FSI computations, ways of accounting for fluid forces acting on structural components that are not expected to influence the flow, adaptive HMGP, and multiscale sequentially coupled FSI techniques. While FSI modeling of complex parachutes was the motivation behind developing some of these techniques, they are also applicable to other classes of complex FSI problems. We also present new ideas to increase the scope of our FSI and CFD techniques. Copyright (C) 2009 John Wiley & Sons, Ltd.