Xiao-Yen Wang

Robust and simple non-reflecting boundary conditions for the space-time conservation element and solution element method

This paper reports on a significant advance in the area of non-reflecting boundary conditions for unsteady flow computations. Sets of new non-reflecting boundary conditions for ID Euler problems are developed without using any characteristics-based techniques. These conditions are much simpler than those commonly reported in the CFD literature, yet so robust that they are applicable to subsonic, transonic and supersonic flows even in the presence of discontinuities. The paper details the theoretical underpinning of the boundary conditions, and explains their unique robustness and accuracy, in terms of the conservation of space-time fluxes. Some numerical results for an extended Sods shock-tube problem, illustrating the effectiveness of the boundary condi* Senior Research Scientist, e-mail: vvscc@noboo.lerc.nasa.gov ^Member, AIAA; e-mail: fshiman@trout.lerc.nasa.gov ^Member, AIAA; e-mail: fsloh@nasp03.lerc.nasa.gov § Member, AIAA, and Research Associate, e-mail: wangxy@rintintin.colorado.edu ^Member, AIAA, and Senior Engineer, e-mail: styu@lerc.nasa.gov II Member, AIAA, and Aerospace Engineer, e-mail: jorgenson@lerc.nasa.gov Copyright ©1997 American Institute of Aeronautics and Astronautics, Inc. No copyright is asserted in the United States under Title 17, U.S. Code. The U.S. Government has a royalty-free license to exercise all rights under the copyright claimed herein for Governmental Purposes. All other rights are reserved by the copyright owner. tions, are included, together with the simple Fortran computer program with which they were obtained. Since the properties of the numerical boundary conditions are closely linked to the previously developed interior schemes, a summary of the interior schemes is also provided.

Local time-stepping procedures for the space-time conservation element and solution element method

A local time-stepping procedure for the space-time conservation element and solution element (CESE) method has been developed. This new procedure allows for variation of time-step size in both space and time, and can also be extended to become multi-dimensional solvers with structured/unstructured spatial grids. Moreover, it differs substantially in concept and methodology from the existing approaches. By taking full advantage of key concepts of the CESE method, in a simple and efficient manner it can enforce flux conservation across an interface separating grid zones of different time-step sizes. In particular, no correction pass is needed. Numerical experiments show that, for a variety of flow problems involving moving shock and flame discontinuities, accurate and robust numerical simulations can be achieved even with a reduction in time-step size on the order of 10 or higher for grids across a single interface.

Development of Parametric Mass and Volume Models for an Aerospace SOFC/Gas Turbine Hybrid System

In aerospace power systems, mass and volume are key considerations to produce a viable design. The utilization of fuel cells is being studied for a commercial aircraft electrical power unit. Based on preliminary analyses [1, 2], a SOFC/gas turbine system may be a potential solution. This paper describes the parametric mass and volume models that are used to assess an aerospace hybrid system design. The design tool utilizes input from the thermodynamic system model and produces component sizing, performance and mass estimates. The software is designed such that the thermodynamic model is linked to the mass and volume model to provide immediate feedback during the design process. It allows for automating an optimization process that accounts for mass and volume in its figure of merit. Each component in the system is modeled with a combination of theoretical and empirical approaches. A description of the assumptions and design analyses is presented.Copyright

The CE/SE Method for Navier-Stokes Equations Using Unstructured Meshes for Flows at All Speeds

In this paper, we report an extension of the Space-Time Conservation Element and Solution Element (CE/SE) Method for solving the Navier-Stokes equations. Numerical algorithms for both structured and unstructured meshes are developed. To calculate the viscous flux terms, a ‘midpoint rule’ is used. In the setting of space-time flux conservation, a new and unified boundary-condition treatment for solid wall is introduced. The Navier Stokes solvers retain all favorable features of the original CE/SE method for the Euler equations, including high fidelity resolution of unsteady flows, easy implementation of nonreflective boundary conditions, and simplicity of computational logic. In addition, numerical results show that the present Navier-Stokes solvers can be used for high-speed flows as well as low-Mach-number flows without preconditioning. The present Navier Stokes solvers are efficient, accurate, and very robust for flows at all speeds.

Prediction of Sound Waves Propagating Through a Nozzle Without/With a Shock Wave Using the Space-Time CE/SE Method

AbstractThe benchmark problems in Category l(InternalPropagation) of the third Computational Aeroacous-tics (CAA) Workshop sponsored by NASA GlennResearch Center are solved using the space-timeconservation element and solution element (CE/SE)method. The first problem addresses the propaga-tion of sound waves through a nearly choked tran-sonic nozzle. The second one concerns shock-soundinteraction in a supersonic nozzle. A quasi 1-DCE/SE Euler solver for a nonuniform mesh is de-veloped and employed to solve both problems. Nu-merical solutions are compared with the analyticalsolution for both problems. It is demonstrated thatthe CE/SE method is capable of soMng aeroacous-tic problems with/without shock waves in a simpleway. Furthermore, the simple non-reflecting bound-ary condition used in the CE/SE method which isnot. based on the characteristic theory works verywell.1. IntroductionThe method of space-time conservation elementand solution element (abbreviated as the CE/SEmethod) is an innovative numerical method for solv-ing conservation laws. It is different in both con-cept and methodology from the well-established tra-ditional methods such as the finite difference, finitevolume, finite element and spectral methods. It isdesigned from a physicists perspective to overcomeseveral key limitations of the traditional numericalmethods.Simplicity, generality and accuracy are weightedin the development of this method while the funda:mental requirements are satisfied by the scheme. Its

Local Mesh Refinement in the Space-Time CE/SE Method

A local mesh refinement procedure for the CE/SE method which does not use an iterative procedure in the treatments of grid-to-grid communications is described. It is shown that a refinement ratio in the order of 10 can be applied successfully across a single coarse grid/fine grid interface.

The method of space-time conservation element and solution element-applications to one-dimensional and two-dimensional time-marching flow problems

A nontraditional numerical method for solving conservation laws is being developed. The new method is designed from a physicists perspective, i.e., its development is based more on physics than numerics. Even though it uses only the simplest approximation techniques, a 2D time-marching Euler solver developed recently using the new method is capable of generating nearly perfect solutions for a 2D shock reflection problem used by Helen Yee and others. Moreover, a recent application of this solver to computational aeroacoustics (CAA) problems reveals that: (i) accuracy of its results is comparable to that of a 6th order compact difference scheme even though nominally the current solver is only of 2nd-order accuracy; (ii) generally, the non-reflecting boundary condition can be implemented in a simple way without involving characteristic variables; and (iii) most importantly, the current solver is capable ofhandling both continuous and discontinuous flows very well and thus provides a unique numerical tool for solving those flow problems where the interactions between sound waves and shocks are important, such as the noise field around a supersonic overor under-expansion jet. *Graduate student, Student member AIAA. _Professor, Associate Fellow AIKA. Copyright (_)1995 by the American Institute of Aeronautics and Astronautics, Inc. No copyright is asserted in the United States under Title 17, U.S. Code. The U.S. Government has a royalty-free license to exercise all rights under the copyright claimed herein for government purposes. All other rights are reserved by the copyright owner. 0\ _ 2.0

Numerical simulation of flows caused by shock-body interaction

Various unsteady flows caused by shock-body interaction are simulated by using a 2-D Euler solver which has been constructed based on the spacetime conservation element and solution element (ST CE/SE) method. The flow phenomena include different types of shock reflection from a wedge in a channel, and interaction of shock waves with stationary and moving bodies resulting in vortices, curved shock waves, contact surfaces, and Mach reflections. Numerical results are compared with experiments and/or numerical results obtained by using some traditional methods to demonstrate the accuracy and simplicity of the S-T CE/SE method. Details of the photographed wave patterns are very well captured in the CE/SE numerical solutions.

Orion Service Module Reaction Control System Plume Impingement Analysis Using PLIMP/RAMP2

The Orion Crew Exploration Vehicle Service Module Reaction Control System engine plume impingement was computed using the plume impingement program (PLIMP). PLIMP uses the plume solution from RAMP2, which is the refined version of the reacting and multiphase program (RAMP) code. The heating rate and pressure (force and moment) on surfaces or components of the Service Module were computed. The RAMP2 solution of the flow field inside the engine and the plume was compared with those computed using GASP, a computational fluid dynamics code, showing reasonable agreement. The computed heating rate and pressure using PLIMP were compared with the Reaction Control System plume model (RPM) solution and the plume impingement dynamics (PIDYN) solution. RPM uses the GASP-based plume solution, whereas PIDYN uses the SCARF plume solution. Three sets of the heating rate and pressure solutions agree well. Further thermal analysis on the avionic ring of the Service Module was performed using MSC Patran/Pthermal. The obtained temperature results showed that thermal protection is necessary because of significant heating from the plume.

Parallel CE/SE Computations via Domain Decomposition

This paper describes the parallelization strategy and achieved parallel efficiency of an explicit time-marching algorithm for solving conservation laws. The Space- Time Conservation Element and Solution Element (CE/SE) algorithm for solving the 2D and 3D Euler equations is parallelized with the aid of domain decomposition. The parallel efficiency of the resultant algorithm on a Silicon Graphics Origin 2000 parallel computer is checked.