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At least 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
NASA NTRS2000

High Order Discontinuous Gelerkin Methods for Convection Dominated Problems with Application to Aeroacoustics

This project is about the investigation of the development of the discontinuous Galerkin finite element methods, for general geometry and triangulations, for solving convection dominated problems, with applications to aeroacoustics. On the analysis side, we have studied the efficient and stable discontinuous Galerkin framework for small second derivative terms, for example in Navier-Stokes equations, and also for related equations such as the Hamilton-Jacobi equations. This is a truly local discontinuous formulation where derivatives are considered as new variables. On the applied side, we have implemented and tested the efficiency of different approaches numerically. Related issues in high order ENO and WENO finite difference methods and spectral methods have also been investigated. Jointly with Hu, we have presented a discontinuous Galerkin finite element method for solving the nonlinear Hamilton-Jacobi equations. This method is based on the RungeKutta discontinuous Galerkin finite element method for solving conservation laws. The method has the flexibility of treating complicated geometry by using arbitrary triangulation, can achieve high order accuracy with a local, compact stencil, and are suited for efficient parallel implementation. One and two dimensional numerical examples are given to illustrate the capability of the method. Jointly with Hu, we have constructed third and fourth order WENO schemes on two dimensional unstructured meshes (triangles) in the finite volume formulation. The third order schemes are based on a combination of linear polynomials with nonlinear weights, and the fourth order schemes are based on combination of quadratic polynomials with nonlinear weights. We have addressed several difficult issues associated with high order WENO schemes on unstructured mesh, including the choice of linear and nonlinear weights, what to do with negative weights, etc. Numerical examples are shown to demonstrate the accuracies and robustness of the methods for shock calculations. Jointly with P. Montarnal, we have used a recently developed energy relaxation theory by Coquel and Perthame and high order weighted essentially non-oscillatory (WENO) schemes to simulate the Euler equations of real gas. The main idea is an energy decomposition under the form epsilon = epsilon(sub 1) + epsilon(sub 2), where epsilon(sub 1) is associated with a simpler pressure law (gamma)-law in this paper) and the nonlinear deviation epsilon(sub 2) is convected with the flow. A relaxation process is performed for each time step to ensure that the original pressure law is satisfied. The necessary characteristic decomposition for the high order WENO schemes is performed on the characteristic fields based on the epsilon(sub l) gamma-law. The algorithm only calls for the original pressure law once per grid point per time step, without the need to compute its derivatives or any Riemann solvers. Both one and two dimensional numerical examples are shown to illustrate the effectiveness of this approach.

Shu, Chi-Wang↗
NASA NTRS1995

Three-dimensional unstructured method for flows past bodies in 6-DOF relative motion

A three dimensional, unstructured-mesh methodology was developed to simulate unsteady flows past bodies in relative motion, where the trajectory was determined from the instantaneous aerodynamics. The method coupled the equations of fluid flow and those of rigid-body dynamics, and captured the time-dependent interference between stationary and moving boundaries. The unsteady, compressible Euler equations were solved on dynamic, unstructured meshes by an explicit, finite-volume, upwind method. The grid adaptation was performed within a window placed around the moving body. The Euler equations of dynamics were solved by a Runge-Kutta integration scheme. The flow solver and the adaptation scheme were validated by simulating the transonic, unsteady flow around a wing undergoing a forced, periodic pitching motion, then comparing the results with the experimental data. To validate the trajectory code, the six-degrees-of-freedom (DOF) motion of a store separating from a wing was computed using the experimentally determined force and moment fields, then comparing with an independently generated trajectory. Finally, the overall methodology was demonstrated by simulating the unsteady flowfield and the trajectory of a store dropped from a wing. The methodology, its computational cost notwithstanding, has proven to be accurate, automated, easy for dynamic gridding, and relatively efficient for the required man-hours.

Singh, K. P.↗
NASA NTRS1994

Analysis and design of numerical schemes for gas dynamics 1: Artificial diffusion, upwind biasing, limiters and their effect on accuracy and multigrid convergence

The theory of non-oscillatory scalar schemes is developed in this paper in terms of the local extremum diminishing (LED) principle that maxima should not increase and minima should not decrease. This principle can be used for multi-dimensional problems on both structured and unstructured meshes, while it is equivalent to the total variation diminishing (TVD) principle for one-dimensional problems. A new formulation of symmetric limited positive (SLIP) schemes is presented, which can be generalized to produce schemes with arbitrary high order of accuracy in regions where the solution contains no extrema, and which can also be implemented on multi-dimensional unstructured meshes. Systems of equations lead to waves traveling with distinct speeds and possibly in opposite directions. Alternative treatments using characteristic splitting and scalar diffusive fluxes are examined, together with modification of the scalar diffusion through the addition of pressure differences to the momentum equations to produce full upwinding in supersonic flow. This convective upwind and split pressure (CUSP) scheme exhibits very rapid convergence in multigrid calculations of transonic flow, and provides excellent shock resolution at very high Mach numbers.

Jameson, Antony↗
NASA NTRSDate not supplied

Derivation of Effective Properties Based on Porous Scale Simulations Using Filtering Techniques

This study presents a method for derivation of effective properties at the interface and in-depth of porous materials. The method defines a Representative Elementary Volume (REV) and applies filtering techniques to computer effective properties such as porosity and flow quantities, such as velocity and pressure. The script, developed to process the data was tested on the VTK type files that contain the mesh information and the flow solution. The method allows to choose between two types of filters, such as cellular and top-hat and define the size of the REV and number of samples along the domain. Extraction of the REV from the domain is performed to exact boundaries requested for the user. This is done using a triangulation technique and cutting through the cells to comply to the requested boundaries of the volume. The method can be applied to both structured and unstructured meshes. Filtering the material porosity and flow quantities involves integration of the numerical data. The algorithm provides three integration methods, such as Riemann sum, Monte Carlo and Quadrature rule to perform the integration. The Monte-Carlo technique permits the use of either uniform or linearly spaced distribution of points. The Quadrature rule is currently applicable to tetrahedral element types. The Monte Carlo and Quadrature rule methods require interpolation of the flow quantities at the sample points. For interpolation, two methods were tested and are readily available, Gaussian interpolation and re-sampling. It has been shown that re-sampling method has better consistency and acceptable accuracy in interpolation of the data. The algorithm was written in Python language and uses a number of modules. The major module besides numpy is PyVista. It is used to process the computational domain, clip the REV and interpolate the data. Quadrature rule integration was performed using a quadpy module. ParaView software was used externally to convert the flow solution to the VTK (or more specifically VTU) format. Integration of ParaView in the same environment with PyVista encountered problems and could not be implemented in this work. The developed algorithm is expected to be applicable to unstructured meshes and more complex porous structures as soon as the data can be passed in VTK type format. With the report is provided Python script for filtering the solution and a Matlab script for simple generation and processing of 2-D and 3-D porous channel geometries. The two scripts don't communicate.

Alexsander Zibitsker↗
NASA NTRS1989

Zonal multigrid solution of compressible flow problems on unstructured and adaptive meshes

The simultaneous use of adaptive meshing techniques with a multigrid strategy for solving the 2-D Euler equations in the context of unstructured meshes is studied. To obtain optimal efficiency, methods capable of computing locally improved solutions without recourse to global recalculations are pursued. A method for locally refining an existing unstructured mesh, without regenerating a new global mesh is employed, and the domain is automatically partitioned into refined and unrefined regions. Two multigrid strategies are developed. In the first, time-stepping is performed on a global fine mesh covering the entire domain, and convergence acceleration is achieved through the use of zonal coarse grid accelerator meshes, which lie under the adaptively refined regions of the global fine mesh. Both schemes are shown to produce similar convergence rates to each other, and also with respect to a previously developed global multigrid algorithm, which performs time-stepping throughout the entire domain, on each mesh level. However, the present schemes exhibit higher computational efficiency due to the smaller number of operations on each level.

Mavriplis, Dimitri J.↗
NASA NTRS1993

An upwind multigrid method for solving viscous flows on unstructured triangular meshes

A multigrid algorithm is combined with an upwind scheme for solving the two dimensional Reynolds averaged Navier-Stokes equations on triangular meshes resulting in an efficient, accurate code for solving complex flows around multiple bodies. The relaxation scheme uses a backward-Euler time difference and relaxes the resulting linear system using a red-black procedure. Roe's flux-splitting scheme is used to discretize convective and pressure terms, while a central difference is used for the diffusive terms. The multigrid scheme is demonstrated for several flows around single and multi-element airfoils, including inviscid, laminar, and turbulent flows. The results show an appreciable speed up of the scheme for inviscid and laminar flows, and dramatic increases in efficiency for turbulent cases, especially those on increasingly refined grids.

Bonhaus, Daryl Lawrence↗
NASA NTRS2003

Unstructured Adaptive Meshes: Bad for Your Memory?

This viewgraph presentation explores the need for a NASA Advanced Supercomputing (NAS) parallel benchmark for problems with irregular dynamical memory access. This benchmark is important and necessary because: 1) Problems with localized error source benefit from adaptive nonuniform meshes; 2) Certain machines perform poorly on such problems; 3) Parallel implementation may provide further performance improvement but is difficult. Some examples of problems which use irregular dynamical memory access include: 1) Heat transfer problem; 2) Heat source term; 3) Spectral element method; 4) Base functions; 5) Elemental discrete equations; 6) Global discrete equations. Nonconforming Mesh and Mortar Element Method are covered in greater detail in this presentation.

Biswas, Rupak↗
NASA NTRS2004

Navier-Stokes Computations of Longitudinal Forces and Moments for a Blended Wing Body

The object of this paper is to investigate the feasibility of applying CFD methods to aerodynamic analyses for aircraft stability and control. The integrated aerodynamic parameters used in stability and control, however, are not necessarily those extensively validated in the state of the art CFD technology. Hence, an exploratory study of such applications and the comparison of the solutions to available experimental data will help to assess the validity of the current computation methods. In addition, this study will also examine issues related to wind tunnel measurements such as measurement uncertainty and support interference effects. Several sets of experimental data from the NASA Langley 14x22-Foot Subsonic Tunnel and the National Transonic Facility are presented. Two Navier-Stokes flow solvers, one using structured meshes and the other unstructured meshes, were used to compute longitudinal static stability derivatives for an advanced Blended Wing Body configuration over a wide range of angles of attack. The computations were performed for two different Reynolds numbers and the resulting forces and moments are compared with the above mentioned wind tunnel data.

Pao, S. Paul↗
NASA NTRS2005

Navier-Stokes Computations of Longitudinal Forces and Moments for a Blended Wing Body

The object of this paper is to investigate the feasibility of applying CFD methods to aerodynamic analyses for aircraft stability and control. The integrated aerodynamic parameters used in stability and control, however, are not necessarily those extensively validated in the state of the art CFD technology. Hence, an exploratory study of such applications and the comparison of the solutions to available experimental data will help to assess the validity of the current computation methods. In addition, this study will also examine issues related to wind tunnel measurements such as measurement uncertainty and support interference effects. Several sets of experimental data from the NASA Langley 14x22-Foot Subsonic Tunnel and the National Transonic Facility are presented. Two Navier-Stokes flow solvers, one using structured meshes and the other unstructured meshes, were used to compute longitudinal static stability derivatives for an advanced Blended Wing Body configuration over a wide range of angles of attack. The computations were performed for two different Reynolds numbers and the resulting forces and moments are compared with the above mentioned wind tunnel data.

Pao, S. Paul↗
NASA NTRSDate not supplied

Anisotropic Goal-Based Mesh Adaptation Metric Clarification and Development

Adaptive unstructured mesh techniques have a limited, but growing impact on production analysis workflows to control discretization error for reliable simulation results. Multiple independent implementations of flow solvers, anisotropic metric construction methods, and anisotropic mesh adaptation mechanics have matured. Goal-based metrics target estimated error in output functions, such as lift and drag, through the guidance of an adjoint solution. A unification of goal-based anisotropic metrics is presented for steady viscous flows, which is an active area of research. These goal-based metrics drive robust and efficient anisotropic mesh adaptation for the calculation of output functions. The super-convergent functional output error behavior of stabilized finite-element methods is exploited without a formal proof, and evidence of super-convergence is shown in numerical experiments. Mesh adapted drag and lift outputs for two simple bodies in compressible viscous flow show convergence of error to less than a single drag count. Asymptotic behavior established for relatively coarse meshes shows the efficiency of this goal-based metric when compared to solution interpolation error control and expert-guided meshing. Anisotropic mesh adaptation techniques are applied to a transport aircraft in a high-lift configuration where variation between approaches decreases with mesh refinement, but asymptotic behavior is not observed with available resources.

goal-based↗