Search NASA⌕ Search

SEARCH · Search NASA

Results for “EULER EQUATION”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 307 records · Page 17
All sourcesNASA NTRSDOE OSTI
NASA NTRS1991

An h-p Taylor-Galerkin finite element method for compressible Euler equations

An extension of the familiar Taylor-Galerkin method to arbitrary h-p spatial approximations is proposed. Boundary conditions are analyzed, and a linear stability result for arbitrary meshes is given, showing the unconditional stability for the parameter of implicitness alpha not less than 0.5. The wedge and blunt body problems are solved with both linear, quadratic, and cubic elements and h-adaptivity, showing the feasibility of higher orders of approximation for problems with shocks.

Demkowicz, L.↗
NASA NTRS1995

The method of space-time and conservation element and solution element: A new approach for solving the Navier-Stokes and Euler equations

A new numerical framework for solving conservation laws is being developed. This new framework differs substantially in both concept and methodology from the well-established methods, i.e., finite difference, finite volume, finite element, and spectral methods. It is conceptually simple and designed to overcome several key limitations of the above traditional methods. A two-level scheme for solving the convection-diffusion equation is constructed and used to illuminate the major differences between the present method and those previously mentioned. This explicit scheme, referred to as the a-mu scheme, has two independent marching variables.

Chang, Sin-Chung↗
NASA NTRS1997

Variational Methods in Design Optimization and Sensitivity Analysis for Two-Dimensional Euler Equations

Variational methods (VM) sensitivity analysis employed to derive the costate (adjoint) equations, the transversality conditions, and the functional sensitivity derivatives. In the derivation of the sensitivity equations, the variational methods use the generalized calculus of variations, in which the variable boundary is considered as the design function. The converged solution of the state equations together with the converged solution of the costate equations are integrated along the domain boundary to uniquely determine the functional sensitivity derivatives with respect to the design function. The application of the variational methods to aerodynamic shape optimization problems is demonstrated for internal flow problems at supersonic Mach number range. The study shows, that while maintaining the accuracy of the functional sensitivity derivatives within the reasonable range for engineering prediction purposes, the variational methods show a substantial gain in computational efficiency, i.e., computer time and memory, when compared with the finite difference sensitivity analysis.

Ibrahim, A. H.↗
NASA NTRS1981

Two-Dimensional Unsteady Euler-Equation Solver for Arbitrarily Shaped Flow Regions

A new technique is described for solving supersonic fluid dynamics problems containing multiple regions of continuous flow, each bounded by a permeable or impermeable surface. Region boundaries are, in general, arbitrarily shaped and time dependent. Discretization of such a region for solution by conventional finite difference procedures is accomplished using an elliptic solver which alleviates the dependence on a particular base coordinate system. Multiple regions are coupled together through the boundary conditions. The technique has been applied to a variety of problems including a shock diffraction problem and supersonic flow over a pointed ogive.

Hindman, R. G.↗
NASA NTRS1985

A Relaxation Approach to Patched-Grid Calculations with the Euler Equations

A conservative zonal-boundary condition that was used with explicit integration schemes is extended to implicit, upwind, relaxation schemes; in particular to the Osher scheme, The rate of convergence was found to increase considerably with the use of the implicit, relaxation-zonal-scheme when compared to the explicit scheme. The relaxation-zonal scheme has also been used in a time-accurate mode. Results demonstrating the time accuracy of the scheme and the feasibility of performing calculations in cases where some parts of the given system move relative to others (e.g., rotor-stator configurations) are presented.

Rai, Man Mohan↗
NASA NTRS1986

An Implicit, Conservative, Zonal-Boundary Scheme for Euler Equation Calculations

A "zonal," or "patched-grid," approach is one in which the flow region of interest is divided into subregions which are then discretized independently, using existing grid generators. The equations of motion are integrated in each subregion in conjunction with zonal-boundary schemes which allow proper information transfer across interfaces that separate subregions. The zonal approach greatly simplifies the treatment of complex geometries and also the addition of grid points to selected regions of the flow. In this study a conservative, zonal-boundary condition that could be used with explicit schemes has been extended so that it can be used with existing second-order accurate implicit integration schemes such as the Beam-Warming and Osher schemes. In the test case considered, the implicit schemes increased the rate of convergence considerably (by a factor of about 30 over that of the explicit scheme). Results demonstrating the time-accuracy of the zonal scheme and the feasibility of performing calculations on zones that move relative to each other are also presented.

Rai, Man Mohan↗
NASA NTRS2002

Spectral (Finite) Volume Method for One Dimensional Euler Equations

Consider a mesh of unstructured triangular cells. Each cell is called a Spectral Volume (SV), denoted by Si, which is further partitioned into subcells named Control Volumes (CVs), indicated by C(sub i,j). To represent the solution as a polynomial of degree m in two dimensions (2D) we need N = (m+1)(m+2)/2 pieces of independent information, or degrees of freedom (DOFs). The DOFs in a SV method are the volume-averaged mean variables at the N CVs. For example, to build a quadratic reconstruction in 2D, we need at least (2+1)(3+1)/2 = 6 DOFs. There are numerous ways of partitioning a SV, and not every partition is admissible in the sense that the partition may not be capable of producing a degree m polynomial. Once N mean solutions in the CVs of a SV are given, a unique polynomial reconstruction can be obtained.

Wang, Z. J.↗
NASA NTRS1987

Computation of non-linear acoustics in two-dimensional blade-vortex interactions

The propagation characteristics of the interaction between a vortex and a helicopter airfoil are investigated by a variety of methods, and a comparison is made between solutions to the linearized transonic small disturbance equation, transonic small disturbance equation, Euler equations, and Navier-Stokes equations. Although the first two methods are able to accurately predict the propagation of acoustic waves, they are unable to accurately describe the initial formation of acoustic waves. The Euler and Navier-Stokes equations are shown to be well suited to the investigation of acoustic waves and give approximately the same results.

Baeder, J. D.↗
NASA NTRS1992

Flutter analysis of a supersonic cascade in time domain using an ADI Euler solver

The aeroelastic stability of a two-dimensional cascade oscillating in supersonic axial flow is analyzed in the time domain. The aeroelastic model consists of a single degree of freedom typical section structural model for each blade of the cascade and an unsteady two-dimensional cascade aerodynamic model based on the Euler equations. The Euler equations are solved using a time accurate Alternating Direction Implicit (ADI) solution scheme. The aeroelastic equations are integrated in time. The effect of interblade phase angle is included in the aeroelastic analysis by an appropriate choice of initial and boundary conditions. Flutter predictions are obtained from the time response of a flat plate cascade in single degree of freedom pitching motion. The results correlate well with those obtained from a separate frequency domain flutter analysis for all values of interblade phase angles considered. Flutter results are then presented for cascades having airfoil sections representative of a supersonic throughflow fan. The validity of the time integration method for a cascade of airfoils at various interblade phase angles is demonstrated.

Reddy, T. S. R.↗