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Results for “Compressible Euler Equations”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 181 records · Page 10
All sourcesNASA NTRSDOE OSTI
NASA NTRS1989

Transonic flow solutions using a composite velocity procedure for potential, Euler and RNS equations

Solutions for transonic viscous and inviscid flows using a composite velocity procedure are presented. The velocity components of the compressible flow equations are written in terms of a multiplicative composite consisting of a viscous or rotational velocity and an inviscid, irrotational, potential-like function. This provides for an efficient solution procedure that is locally representative of both asymptotic inviscid and boundary layer theories. A modified conservative form of the axial momentum equation that is required to obtain rotational solutions in the inviscid region is presented and a combined conservation/nonconservation form is applied for evaluation of the reduced Navier-Stokes (RNS), Euler and potential equations. A variety of results is presented and the effects of the approximations on entropy production, shock capturing, and viscous interaction are discussed.

Gordnier, R. E.↗
NASA NTRS1987

Finite Element Flux-Corrected Transport (FEM-FCT) for the Euler and Navier-Stokes equations

A high resolution finite element method for the solution of problems involving high speed compressible flows is presented. The method uses the concepts of flux-corrected transport and is presented in a form which is suitable for implementation on completely unstructured triangular or tetrahedral meshes. Transient and steady state examples are solved to illustrate the performance of the algorithm.

Loehner, Rainald↗
NASA NTRS1987

Finite element flux-corrected transport (FEM-FCT) for the Euler and Navier-Stokes equations

A high resolution finite element method for the solution of problems involving high speed compressible flows is presented. The method uses the concepts of flux-corrected transport and is presented in a form which is suitable for implementation on completely unstructured triangular or tetrahedral meshes. Transient and steady-state examples are solved to illustrate the performance of the algorithm.

Lohner, Rainald↗
NASA NTRS1988

Finite element solution of the Euler equations in two and three dimensions

The paper presents a finite element procedure for solving the equations of compressible flow over bodies of arbitrary geometry. The numerical solution algorithm employed is an explicit two-step version of a second order Taylor-Galerkin scheme. The discretization of the computational domain into unstructured meshes of triangles in two dimensions and tetrahedra in three dimensions is performed by an automatic mesh generator. In the approach, the mesh generator is coupled to the finite element solver to produce an adaptive remeshing procedure.

Peiro, J.↗
NASA NTRS1982

Convergence acceleration of viscous flow computations

A multiple-grid convergence acceleration technique introduced for application to the solution of the Euler equations by means of Lax-Wendroff algorithms is extended to treat compressible viscous flow. Computational results are presented for the solution of the thin-layer version of the Navier-Stokes equations using the explicit MacCormack algorithm, accelerated by a convective coarse-grid scheme. Extensions and generalizations are mentioned.

Johnson, G. M.↗
NASA NTRS1983

Compact finite difference schemes for the Euler and Navier-Stokes equations

Implicit compact finite difference schemes for the Euler equations are described which furnish equivalent treatment of the conservation and nonconservation forms; a simple modification yields an entropy-producing scheme. An extension of the scheme also treats the compressible Navier-Stokes equations; when the viscosity and heat conduction coefficients are negligible only the boundary data appropriate to the Euler equation influence the solution to any significant extent, a result consistent with singular perturbation theory.

Rose, M. E.↗
NASA NTRS1997

Airfoil Design Using a Coupled Euler and Integral Boundary Layer Method with Adjoint Based Sensitivities

The objective of this paper is to present a control theory approach for the design of airfoils in the presence of viscous compressible flows. A coupled system of the integral boundary layer and the Euler equations is solved to provide rapid flow simulations. An adjunct approach consistent with the complete coupled state equations is employed to obtain the sensitivities needed to drive a numerical optimization algorithm. Design to target pressure distribution is demonstrated on an RAE 2822 airfoil at transonic speed.

Edwards, S.↗
NASA NTRS1987

Adaptive remeshing for compressible flow computations

The present, quality-enhancing adaptive-mesh procedure for two-dimensional Euler equation steady state solutions is implemented by means of linear triangular elements and an explicit time-stepping scheme, in conjunction with a finite element solution algorithm. The meshes thus generated typically take the form of stretched elements in the vicinity of one-dimensional flow features; a considerable variation in element size may thereby emerge which allows the desired high-quality solutions to be obtained with commensurately high computational efficiency.

Peraire, J.↗
NASA NTRS1986

Coupling between fluid dynamics and energy addition in arcjet and microwave thrusters

A new approach to numerically solving the problem of the constricted electric arcjet is presented. An Euler Implicit finite difference scheme is used to solve the full compressible Navier Stokes equations in two dimensions. The boundary and initial conditions represent the constrictor section of the arcjet, and hydrogen is used as a propellant. The arc is modeled as a Gaussian distribution across the centerline of the constrictor. Temperature, pressure and velocity profiles for steady state converged solutions show both axial and radial changes in distributions resulting from their interaction with the arc energy source for specific input conditions. The temperature rise is largest at the centerline where there is a the greatest concentration arc energy. The solution does not converge for all initial inputs and the limitations in the range of obtainable solutions are discussed.

Micci, M. M.↗
NASA NTRS1992

Unsteady blade pressures on a propfan: Predicted and measured compressibility effects

The effect of compressibility on unsteady blade pressures is studied by solving the three-dimensional Euler equations. The operation of the eight-bladed SR7L propfan at a 4.75 deg angle of attack was considered. Euler solutions were obtained for three Mach numbers, 0.6, 0.7 and 0.8, and the predicted blade pressure waveforms were compared with flight data. The comparisons show that in general, the effect of Mach number on pressure waveforms are correctly predicted. The change in pressure waveforms are minimal when the Mach number is increased from 0.6 to 0.7. Increasing the Mach number from 0.7 to 0.8 produces significant changes in predicted pressure levels. The predicted amplitudes, however, differ from measurements at some transducer locations. At all the three Mach numbers, the measured (installed propfan) pressure waveforms show a relative phase lag compared to the computed (propfan along) waveforms due to installation effects. Measured waveforms in the blade tip region show nonlinear variations which are not captured by the present numerical procedure.

Nallasamy, M.↗
NASA NTRS1990

PROTEUS two-dimensional Navier-Stokes computer code, version 1.0. Volume 1: Analysis description

A new computer code was developed to solve the two-dimensional or axisymmetric, Reynolds averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The thin-layer or Euler equations may also be solved. Turbulence is modeled using an algebraic eddy viscosity model. The objective was to develop a code for aerospace applications that is easy to use and easy to modify. Code readability, modularity, and documentation were emphasized. The equations are written in nonorthogonal body-fitted coordinates, and solved by marching in time using a fully-coupled alternating direction-implicit procedure with generalized first- or second-order time differencing. All terms are linearized using second-order Taylor series. The boundary conditions are treated implicitly, and may be steady, unsteady, or spatially periodic. Simple Cartesian or polar grids may be generated internally by the program. More complex geometries require an externally generated computational coordinate system. The documentation is divided into three volumes. Volume 1 is the Analysis Description, and describes in detail the governing equations, the turbulence model, the linearization of the equations and boundary conditions, the time and space differencing formulas, the ADI solution procedure, and the artificial viscosity models.

Towne, Charles E.↗
NASA NTRS1990

PROTEUS two-dimensional Navier-Stokes computer code, version 1.0. Volume 2: User's guide

A new computer code was developed to solve the two-dimensional or axisymmetric, Reynolds averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The thin-layer or Euler equations may also be solved. Turbulence is modeled using an algebraic eddy viscosity model. The objective was to develop a code for aerospace applications that is easy to use and easy to modify. Code readability, modularity, and documentation were emphasized. The equations are written in nonorthogonal body-fitted coordinates, and solved by marching in time using a fully-coupled alternating direction-implicit procedure with generalized first- or second-order time differencing. All terms are linearized using second-order Taylor series. The boundary conditions are treated implicitly, and may be steady, unsteady, or spatially periodic. Simple Cartesian or polar grids may be generated internally by the program. More complex geometries require an externally generated computational coordinate system. The documentation is divided into three volumes. Volume 2 is the User's Guide, and describes the program's general features, the input and output, the procedure for setting up initial conditions, the computer resource requirements, the diagnostic messages that may be generated, the job control language used to run the program, and several test cases.

Towne, Charles E.↗
NASA NTRS1990

PROTEUS two-dimensional Navier-Stokes computer code, version 1.0. Volume 3: Programmer's reference

A new computer code was developed to solve the 2-D or axisymmetric, Reynolds-averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The thin-layer or Euler equations may also be solved. Turbulence is modeled using an algebraic eddy viscosity model. The objective was to develop a code for aerospace applications that is easy to use and easy to modify. Code readability, modularity, and documentation were emphasized. The equations are written in nonorthogonal body-fitted coordinates, and solved by marching in time using a fully-coupled alternating-direction-implicit procedure with generalized first- or second-order time differencing. All terms are linearized using second-order Taylor series. The boundary conditions are treated implicitly, and may be steady, unsteady, or spatially periodic. Simple Cartesian or polar grids may be generated internally by the program. More complex geometries require an externally generated computational coordinate system. The documentation is divided into three volumes. Volume 3 is the Programmer's Reference, and describes the program structure, the FORTRAN variables stored in common blocks, and the details of each subprogram.

Towne, Charles E.↗
NASA NTRS1979

Calculated global conditions for the unsteady Euler's flow equations

This paper considers the numerical solution of a fluid dynamical system with time-dependent oscillating boundaries. The problem detailed, a compressible and inviscid flow in a one-dimensional pipe with vibrating ends, is examined to develop techniques needed to solve the more complex unsteady flows in turbomachine cascades. The problem is shown to be mathematically ill-posed but by complementing the governing equations with energy conservation, a unique solution is obtained. An artificial damping term is introduced into the governing equations to improve the performance of the time-marching integration.

Kuzo, D. M.↗
NASA NTRS1990

A review of reduced Navier-Stokes computations for compressible viscous flows

A reduced form of the Navier-Stokes equations, defined by a single composite of the Euler, boundary layer, and triple deck approximations, is considered for the computation of viscous interacting flows. Global pressure or pseudopotential relaxation methods are integrated with coupled sparse matrix direct solvers or coupled strongly implicit ILU algorithms to efficiently capture sharp shocks and regions of recirculation. Solutions are obtained for a variety of 2D and 3D geometries and for Mach numbers (M) spanning the range from incompressible (M = 0) to supersonic (M = 6) flow.

Rubin, S. G.↗
NASA NTRS1985

Numerical solution of Euler's equation by perturbed functionals

A perturbed functional iteration has been developed to solve nonlinear systems. It adds at each iteration level, unique perturbation parameters to nonlinear Gauss-Seidel iterates which enhances its convergence properties. As convergence is approached these parameters are damped out. Local linearization along the diagonal has been used to compute these parameters. The method requires no computation of Jacobian or factorization of matrices. Analysis of convergence depends on properties of certain contraction-type mappings, known as D-mappings. In this article, application of this method to solve an implicit finite difference approximation of Euler's equation is studied. Some representative results for the well known shock tube problem and compressible flows in a nozzle are given.

Dey, S. K.↗
NASA NTRS1985

An adaptive finite element procedure for compressible high speed flows

A practical finite element-based solution procedure for high-speed inviscid compressible flow problems is described. The method provides time-accurate solutions to the coompressible Euler equations, and is computationally more efficient than the one-step Taylor-Galerkin approach and better suited for implementation on the modern generation of vector computers. The method is coupled to an adaptive mesh refinement process that enables steady state solutions of improved quality to be obtained.

Loehner, R.↗