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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 109 records · Page 6
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NASA NTRS1984

Conservative streamtube solution of steady-state Euler equations

This paper presents a new method for solving the steady state Euler equations. The method is similar to streamline curvature methods but has a conserative finite volume formulation which ensures correct shock capturing. Either wall position or wall pressure may be prescribed as boundary conditions, permitting both direct and inverse calculations. In supersonic applications the solution is obtained by space-marching while in subsonic and transonic applications iterative relaxation methods are used. Numerical results are given for: (1) supersonic diffuser with oblique shocks (direct calculation); (2) supersonic jet entering still reservoir (inverse calculation); (3) subsonic bump in a channel with 25 percent blockage (direct and inverse); (4) subsonic high-work turbine cascade (direct); and (5) transonic bump in a channel with 12 percent blockage (direct calculation).

Drela, M.↗
NASA NTRS1985

Acceleration to a steady state for the Euler equations

A multistage Runge-Kutta method is analyzed for solving the Euler equations exterior to an airfoil. Highly subsonic, transonic and supersonic flows are evaluated. Various techniques for accelerating the convergence to a steady state are introduced and analyzed.

Turkel, E.↗
NASA NTRS1982

A zonal approach to solution of the Euler equations

A technique for the solution of the one- and two-dimensional Euler equations in a partitioned flow field is presented. The field is divided into distinct 'zones', each of which is computed separately. An implicit boundary procedure based on the characteristic propagaion of information and flux splitting methods is applied at the zonal interfaces. Numerical results are presented for both quasi-one-dimensional nozzle flows with shock waves and the unsteady shock-tube problem. These calculations demonstrate the capability of shock propagation through arbitrarily located zonal boundaries in a stable, conservative, and accurate manner. Two-dimensional results include the zonal computation of flows over blunt bodies and airfoils.

Hessenius, K. A.↗
NASA NTRS1982

Application of a finite element algorithm for the solution of steady transonic Euler equations

A finite element algorithm for the solution of two-dimensional, steady Euler equations is presented which, through a Clebsch-type transformation for the velocity vector, solves the conservation of mass equation with one primary variable and two additional equations for the convection of two new variables. The accuracy and efficiency of this scheme is discussed, and the second-order accuracy attained in the analysis of the convection of the vorticity is demonstrated together with the efficient treatment of rotational and irrotational flow subregions. A sample problem is used to show the accuracy of the numerical scheme and its convergence characteristics.

Akay, H. U.↗
NASA NTRS1983

Implicit conservative characteristic modeling schemes for the Euler equations - A new approach

An implicit characteristic-modeling solution scheme for the Euler equations is presented. The scheme does not require the governing equations to be written in characteristic variables or the flux terms to be split into positive and negative contributions. For the two-dimensional problem of a shock wave reflecting from a flat plate, this feature and the simple solution algorithm combine to reduce the computational work per mesh point by 40 percent from that required by a standard, central-difference, implicit, solution algorithm. Application of the method to the quasi-one-dimensional nozzle flow equations for subsonic and supersonic flows without shocks shows the method to be well-conditioned for large time steps.

Wornom, S. F.↗
NASA NTRS1983

Automatic adaptive grid refinement for the Euler equations

A method of adaptive grid refinement for the solution of the steady Euler equations for transonic flow is presented. Algorithm automatically decides where the coarse grid accuracy is insufficient, and creates locally uniform refined grids in these regions. This typically occurs at the leading and trailing edges. The solution is then integrated to steady state using the same integrator (FLO52) in the interior of each grid. The boundary conditions needed on the fine grids are examined and the importance of treating the fine/coarse grid inerface conservatively is discussed. Numerical results are presented.

Berger, M. J.↗
NASA NTRS1984

A Newton multigrid method for the Euler equations

A multigrid method is used to apply Newton's method to the Euler equations in a two dimensional curvilinear coordinate system. The objective is to obtain rapid convergence for steady state problems. Solutions computed with the method evolve in a non-time-like manner. Stable pressure distributions typically develop in eight to ten Newton-multigrid steps, which is equivalent to the computational work of about 70 iterations with a factored implicit algorithm.

Childs, R. E.↗
NASA NTRS1985

Automatic adaptive grid refinement for the Euler equations

A method of adaptive grid refinement for the solution of the steady Euler equations for transonic flow is presented. Algorithm automatically decides where the coarse grid accuracy is insufficient, and creates locally uniform refined grids in these regions. This typically occurs at the leading and trailing edges. The solution is then integrated to steady state using the same integrator (FL052) in the interior of each grid. The boundary conditions needed on the fine grids are examined and the importance of treating the fine/coarse grid interface conservatively is discussed. Numerical results are presented.

Berger, M. J.↗
NASA NTRS1991

Calculation Of Aeroelastic Transients Using Euler Equations

Method for calculation of transient aeroelastic effects on airplane wings based on Euler equations of flow. Conforming grids facilitate calculations of flows about changing shapes. Capability to compute aeroelastic effects reduces cost of developing aircraft.

Guruswamy, Guru P.↗
NASA NTRS1992

Grid generation and flow solution method for Euler equations on unstructured grids

A grid generation and flow solution algorithm for the Euler equations on unstructured grids is presented. The grid generation scheme, which uses Delaunay triangulation, generates the field points for the mesh based on cell aspect ratios and allows clustering of grid points near solid surfaces. The flow solution method is an implicit algorithm in which the linear set of equations arising at each time step is solved using a Gauss-Seidel procedure that is completely vectorizable. Also, a study is conducted to examine the number of subiterations required for good convergence of the overall algorithm. Grid generation results are shown in two dimensions for an NACA 0012 airfoil as well as a two element configuration. Flow solution results are shown for a two dimensional flow over the NACA 0012 airfoil and for a two element configuration in which the solution was obtained through an adaptation procedure and compared with an exact solution. Preliminary three dimensional results also are shown in which the subsonic flow over a business jet is computed.

Anderson, W. Kyle↗
NASA NTRS1992

A 3D finite element multigrid solver for the Euler equations

A low storage, computationally efficient algorithm for the solution of the compressible Euler equations on unstructured tetrahedral meshes is developed. The algorithm takes the form of a centered scheme with the explicit addition of a high accuracy artificial viscosity and the solution is advanced to steady state by means of a multistage timestepping method. The side-based data structure which is employed enables a clear connection to be established between the proposed algorithm and upwind cell vertex schemes for unstructured meshes. The computational efficiency of the procedure is improved by incorporating an unstructured multigrid acceleration procedure. A number of flows of practical interest are analyzed to demonstrate the numerical performance of the proposed approach.

Peraire, J.↗
NASA NTRS1994

A grid generation and flow solution method for the Euler equations on unstructured grids

A grid generation and flow solution algorithm for the Euler equations on unstructured grids is presented. The grid generation scheme utilizes Delaunay triangulation and self-generates the field points for the mesh based on cell aspect ratios and allows for clustering near solid surfaces. The flow solution method is an implicit algorithm in which the linear set of equations arising at each time step is solved using a Gauss Seidel procedure which is completely vectorizable. In addition, a study is conducted to examine the number of subiterations required for good convergence of the overall algorithm. Grid generation results are shown in two dimensions for a National Advisory Committee for Aeronautics (NACA) 0012 airfoil as well as a two-element configuration. Flow solution results are shown for two-dimensional flow over the NACA 0012 airfoil and for a two-element configuration in which the solution has been obtained through an adaptation procedure and compared to an exact solution. Preliminary three-dimensional results are also shown in which subsonic flow over a business jet is computed.

Anderson, W. Kyle↗
NASA NTRS1983

A new stream function formulation for the Euler equations

A new stream function formulation is developed for the solution of Euler's equations in the transonic flow region. The stream function and the density are the dependent variables in this method, while the governing equations for adiabatic flow are the momentum equations which are solved in the strong conservation law form. The application of this method does not require a knowledge of the vorticity. The algorithm is combined with the automatic grid solver (GRAPE) of Steger and Sorenson (1979) in order to study arbitrary geometries. Results of the application of this method are presented for the NACA 0012 airfoil at various Mach numbers and angles of attack, and cylinders. In addition, detailed comparisons are made with other solutions of the Euler equations.

Atkins, H. L.↗
NASA NTRS1990

Adaptive grid embedding for the two-dimensional flux-split Euler equations

A numerical algorithm is presented for solving the 2-D flux-split Euler equations using a multigrid method with adaptive grid embedding. The method uses an unstructured data set along with a system of pointers for communication on the irregularly shaped grid topologies. An explicit two-stage time advancement scheme is implemented. A multigrid algorithm is used to provide grid level communication and to accelerate the convergence of the solution to steady state. Results are presented for a subcritical airfoil and a transonic airfoil with 3 levels of adaptation. Comparisons are made with a structured upwind Euler code which uses the same flux integration techniques of the present algorithm. Good agreement is obtained with converged surface pressure coefficients. The lift coefficients of the adaptive code are within 2 1/2 percent of the structured code for the sub-critical case and within 4 1/2 percent of the structured code for the transonic case using approximately one-third the number of grid points.

Warren, Gary Patrick↗
NASA NTRS1984

Acceleration to a steady state for the Euler equations

A multi-stage Runge-Kutta method is analyzed for solving the Euler equations exterior to an airfoil. Highly subsonic, transonic and supersonic flows are evaluated. Various techniques for accelerating the convergence to a steady state are introduced and analyzed.

Turkel, E.↗
NASA NTRS1984

Flux-vector splitting and Runge-Kutta methods for the Euler equations

Runge-Kutta schemes have been used as a method of solving the Euler equations exterior to an airfoil. In the past this has been coupled with central differences and an artificial vesocity in space. In this study the Runge-Kutta time-stepping scheme is coupled with an upwinded space approximation based on flux-vector splitting. Several acceleration techniques are also considered including a local time step, residual smoothing and multigrid.

Turkel, E.↗
NASA NTRS1985

Artificial dissipation models for the Euler equations

Various artificial dissipation models which are used with central difference algorithms for the Euler equations are analyzed for their effect on accuracy, stability and convergence rates. In particular, linear and nonlinear models are investigated using an implicit approximate factorization code (ARC2D) for transonic airfoils. Fully implicit application of the dissipation models is shown to improve robustness and convergence rates. The treatment of dissipation models at boundaries will be examined. It will be shown that accurate, error free solutions with sharp shocks can be obtained using a central difference algorithm coupled with an appropriate nonlinear artificial dissipation model.

Pulliam, T. H.↗