Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “implicit methods”

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 685 records · Page 38
All sourcesNASA NTRSDOE OSTI
NASA NTRS1992

Nonlinearly stable compact schemes for shock calculations

The applications of high-order, compact finite difference methods in shock calculations are discussed. The main concern is to define a local mean which will serve as a reference for introducing a local nonlinear limiting to control spurious numerical oscillations while maintaining the formal accuracy of the scheme. For scalar conservation laws, the resulting schemes can be proven total-variation stable in one space dimension and maximum-norm stable in multiple space dimensions. Numerical examples are shown to verify accuracy and stability of such schemes for problems containing shocks. These ideas can also be applied to other implicit schemes such as the continuous Galerkin finite element methods.

Cockburn, Bernardo↗
NASA NTRS1986

Self-adaptive difference method for the effective solution of computationally complex problems of boundary layer theory

An implicit difference procedure for the solution of equations for a chemically reacting hypersonic boundary layer is described. Difference forms of arbitrary error order in the x and y coordinate plane were used to derive estimates for discretization error. Computational complexity and time were minimized by the use of this difference method and the iteration of the nonlinear boundary layer equations was regulated by discretization error. Velocity and temperature profiles are presented for Mach 20.14 and Mach 18.5; variables are velocity profiles, temperature profiles, mass flow factor, Stanton number, and friction drag coefficient; three figures include numeric data.

Schoenauer, W.↗
NASA NTRS1991

A Fourier collocation time domain method for numerically solving Maxwell's equations

A new method for solving Maxwell's equations in the time domain for arbitrary values of permittivity, conductivity, and permeability is presented. Spatial derivatives are found by a Fourier transform method and time integration is performed using a second order, semi-implicit procedure. Electric and magnetic fields are collocated on the same grid points, rather than on interleaved points, as in the Finite Difference Time Domain (FDTD) method. Numerical results are presented for the propagation of a 2-D Transverse Electromagnetic (TEM) mode out of a parallel plate waveguide and into a dielectric and conducting medium.

Shebalin, John V.↗
NASA NTRS1983

Improving the convergence rate of parabolic ADI methods

The rate of convergence to steady state of parabolic Alternating Direction Implicit (ADI) solvers is analyzed in terms of the L(2)-norms of the residuals. The analysis allows one to predict the number of iterations necessary for convergence as function of the Courant number, Lambda. A simple modification of existing ADI codes is devised. It improves the convergence rate substantially and is insensitive to the Courant number in a large range of Lambda.

Abarbanel, S. S.↗
NASA NTRS1989

Analysis of a second-order-accurate finite-volume method for temporally-growing compressible shear layers

A finite-volume method for solving the compressible laminar Navier-Stokes equation in two dimensions is assessed for use in the simulation of transitional flows. The method is second-order-accurate, uses alternating-direction-implicit time integration, and a total-variation-diminishing smoothing operator in the inviscid flux terms. The test problem was a free shear layer with a forced periodicity in x at a specified wavelength and with the parallel mean flow specified as a hyperbolic-tangent profile. A grid refinement investigation verified this method to be second-order-accurate with less than 4 percent error in the growth rate of isolated modes on a 32 by 64 grid. The interaction between modes of similar amplitude was small, less than 1 percent. However, in cases where there was a dominant mode, numerical phase error pumped energy into all other modes. This error results in nonphysical growth rate for modes whose energy content is several orders of magnitude below the dominant mode. In the case when the dominant mode saturates, the pumping action stops and the growth rate of the next largest growing mode regains physical significance.

Atkins, H. L.↗
NASA NTRS1991

A Fourier-Chebyshev pseudospectral method for solving steady 3-D Navier-Stokes and heat equations in cylindrical cavities

A Fourier-Chebyshev pseudospectral method for solving steady 3D Navier-Stokes equations in cylindrical cavities is presented and discussed. The general method is pseudo-unsteady and uses a semi-implicit finite difference scheme for the time discretization. The generalized ADI (Alternating Direction Implicit) procedure is then applied to reduce the problem to a successive solution of one-dimensional problems. The spatial approximation uses a Fourier-Galerkin approximation in the periodic direction and a Chebyshev-collocation approximation in the other directions. Difficulties related to the pressure are surmounted by using the artifical compressibility method. A suitable variable change was chosen to avoid the problem of singularity at the axis generated by cylindrical coordinates. The method is first tested on an advection-diffusion equation and then on the Navier-Stokes equations. Finally, the method is illustrated by a convection problem of a differentially heated fluid.

Pulicani, J. P.↗
NASA NTRS1989

On finite element implementation and computational techniques for constitutive modeling of high temperature composites

The research work performed during the past year on finite element implementation and computational techniques pertaining to high temperature composites is outlined. In the present research, two main issues are addressed: efficient geometric modeling of composite structures and expedient numerical integration techniques dealing with constitutive rate equations. In the first issue, mixed finite elements for modeling laminated plates and shells were examined in terms of numerical accuracy, locking property and computational efficiency. Element applications include (currently available) linearly elastic analysis and future extension to material nonlinearity for damage predictions and large deformations. On the material level, various integration methods to integrate nonlinear constitutive rate equations for finite element implementation were studied. These include explicit, implicit and automatic subincrementing schemes. In all cases, examples are included to illustrate the numerical characteristics of various methods that were considered.

Saleeb, A. F.↗
NASA NTRS1993

The effect of Reynolds number and turbulence on airfoil aerodynamics at -90 degrees incidence

A method has been developed for calculating the viscous flow about airfoils in with and without deflected flaps at -90 deg incidence. This method provides for the solution of the unsteady incompressible Navier-Stokes equations by means of an implicit technique. The solution is calculated on a body-fitted computational mesh using a staggered grid method. The vorticity is defined at the node points, and the velocity components are defined at the mesh-cell sides. The staggered-grid orientation provides for accurate representation of vorticity at the node points and the continuity equation at the mesh-cell centers. The method provides for the direct solution of the flow field and satisfies the continuity equation to machine zero at each time-step. The method is evaluated in terms of its ability to predict two-dimensional flow about an airfoil at -90 degrees incidence for varying Reynolds number and different boundary layer models. A laminar and a turbulent boundary layer models. A laminar and a turbulent boundary layer model are considered in the evaluation of the method. The variation of the average loading and surface pressure distribution due to flap deflection, Reynolds number, and laminar or turbulent flow are presented and compared with experimental results. The comparisons indicate that the calculated drag and drag reduction caused by flap deflection and the calculated average surface pressure are in excellent agreement with the measured results at a similar Reynolds number.

Stremel, Paul M.↗
NASA NTRS2013

Design of a Variational Multiscale Method for Turbulent Compressible Flows

A spectral-element framework is presented for the simulation of subsonic compressible high-Reynolds-number flows. The focus of the work is maximizing the efficiency of the computational schemes to enable unsteady simulations with a large number of spatial and temporal degrees of freedom. A collocation scheme is combined with optimized computational kernels to provide a residual evaluation with computational cost independent of order of accuracy up to 16th order. The optimized residual routines are used to develop a low-memory implicit scheme based on a matrix-free Newton-Krylov method. A preconditioner based on the finite-difference diagonalized ADI scheme is developed which maintains the low memory of the matrix-free implicit solver, while providing improved convergence properties. Emphasis on low memory usage throughout the solver development is leveraged to implement a coupled space-time DG solver which may offer further efficiency gains through adaptivity in both space and time.

Design↗
NASA NTRS1989

A new uniformly valid asymptotic integration algorithm for elasto-plastic-creep and unified viscoplastic theories including continuum damage

A new scheme to integrate a system of stiff differential equations for both the elasto-plastic creep and the unified viscoplastic theories is presented. The method has high stability, allows large time increments, and is implicit and iterative. It is suitable for use with continuum damage theories. The scheme was incorporated into MARC, a commercial finite element code through a user subroutine called HYPELA. Results from numerical problems under complex loading histories are presented for both small and large scale analysis. To demonstrate the scheme's accuracy and efficiency, comparisons to a self-adaptive forward Euler method are made.

Chulya, A.↗
NASA NTRS1991

A new uniformly valid asymptotic integration algorithm for elasto-plastic creep and unified viscoplastic theories including continuum damage

A new scheme to integrate a system of stiff differential equations for both the elasto-plastic creep and the unified viscoplastic theories is presented. The method has high stability, allows large time increments, and is implicit and iterative. It is suitable for use with continuum damage theories. The scheme was incorporated into MARC, a commercial finite element code through a user subroutine called HYPELA. Results from numerical problems under complex loading histories are presented for both small and large scale analysis. To demonstrate the scheme's accuracy and efficiency, comparisons to a self-adaptive forward Euler method are made.

Chulya, Abhisak↗
NASA NTRS1994

Effect of Reynolds number and turbulence on airfoil aerodynamics at -90-degree incidence

A method has been developed for calculating the viscous flow about airfoils with and without deflected flaps at -90 deg incidence. This method provides for the solution of the unsteady incompressible Navier-Stokes equations by means of an implicit technique. The solution is calculated on a body-fitted computational mesh using a staggered-grid method. The vorticity is defined at the node points, and the velocity components are defined at the mesh-cell sides. The staggered-grid orientation provides for accurate representation of vorticity at the node points and the continuity equation at the mesh-cell centers. The method provides for the noniterative solution of the flowfield and satisfies the continuity equation to machine zero at each time step. The method is evaluated in terms of its stability to predict two-dimensional flow about an airfoil at -90-deg incidence for varying Reynolds number and laminar/turbulent models. The variations of the average loading and surface pressure distribution due to flap deflection, Reynolds number, and laminar or turbulent flow are presented and compared with experimental results. The comparisom indicate that the calculated drag and drag reduction caused by flap deflection and the calculated average surface pressure are in excellent agreement with the measured results at a similar Reynolds number.

Stremel, Paul M.↗
NASA NTRS1990

Improved boundary layer heat transfer calculations near a stagnation point

A thermal design of a solar receiver has been developed for the solutions of problems involving phase-change thermal energy storage and natural convection loss. Two dimensional axisymmetrical solidification and melting of materials contained between two concentric cylinders of finite length has been studied for thermal energy storage analysis. For calculation of free convection loss inside receiver cavity, two dimensional axisymmetrical, laminar, transient free convection including radiation effects has been studied using integral/finite difference method. Finite difference equations are derived for the above analysis subject to constant or variable material properties, initial conditions, and boundary conditions. The validity of the analyses has been substantiated by comparing results of the present general method with available analytic solutions or numerical results reported in the literature. Both explicit and implicit schemes are tested in phase change analysis with different number of nodes ranging from 4 to 18. The above numerical methods have been applied to the existing solar receiver analyzing computer code as additional subroutines. The results were computed for one of the proposed Brayton cycle solar receiver models running under the actual environmental conditions. Effect of thermal energy storage on the thermal behavior of the receiver has been estimated. Due to the thermal energy storage, about 65% reduction on working gas outlet temperature fluctuation has been obtained; however, maximum temperature of thermal energy storage containment has been increased about 18%. Also, effect of natural convection inside a receiver cavity on the receiver heat transfer has been analyzed. The finding indicated that thermal stratification occurs during the sun time resulting in higher receiver temperatures at the outlet section of the gas tube, and lower temperatures at the inlet section of the gas tube when compared with the results with no natural convection. Due to heat supply from the air during the shade time, minimum temperature has been increased, while maximum temperature has been reduced due to convection loss to air. Consequently, cyclic temperature fluctuation has been reduced 29% for working gas and 16% for thermal energy storage containment. On the other hand, despite the presence of the natural convection the time-averaged temperatures for receiver components were found to be similar for two cases with/without natural convection (maximum difference was 1.8%).

Ahn, Kyung Hwan↗
NASA NTRS1991

Computational study of three dimensional viscous flow through a turbine cascade using a multi-domain spectral technique

The three dimensional viscous flow through a planar turbine cascade is numerically simulated by direct solution of the incompressible Navier-Stokes equations. Flow dependence in the spanwise direction is represented by direct expansion in Chebyshev polynomials, while the discretization on planes parallel to the endwalls is accomplished using the spectral element method. Elemental mapping from the physical to the computational space uses an algebraic mapping technique. A fractional time stepping method that consists of an explicit nonlinear convective step, an implicit pressure correction step, and an implicit viscous step is used to advance the Navier-Stokes equations forward in time. Results computed at moderate Reynolds numbers show a three dimensional endwall flow separation, a midspan separation of the blade suction surface boundary layer, and other three-dimensional features such as the presence of a saddle point flow in the endwall region. In addition, the computed skin friction lines are shown to be orthogonal to the surface vorticity lines, demonstrating the accuracy achievable in the present method.

Renaud, Earl W.↗
NASA NTRS1991

Calculation of unsteady airfoil loads with and without flap deflection at -90 degrees incidence

A method has been developed for calculating the viscous flow about airfoils with and without deflected flaps at -90 deg incidence. This unique method provides for the direct solution of the incompressible Navier-Stokes equations by means of a fully coupled implicit technique. The solution is calculated on a body-fitted computational mesh incorporating a staggered grid method. The vorticity is determined at the node points, and the velocity components are defined at the mesh-cell sides. The staggered-grid orientation provides for accurate representation of vorticity at the node points and for the conservation of mass at the mesh-cell centers. The method provides for the direct solution of the flow field and satisfies the conservation of mass to machine zero at each time-step. The results of the present analysis and experimental results obtained for a XV-15 airfoil are compared. The comparisons indicate that the calculated drag reduction caused by flap deflection and the calculated average surface pressure are in excellent agreement with the measured results. Comparisons of the numerical results of the present method for several airfoils demonstrate the significant influence of airfoil curvature and flap deflection on the predicted download.

Stremel, Paul M.↗
NASA NTRS1978

Calculation of supersonic viscous flow over delta wings with sharp subsonic leading edges

Two complementary procedures were developed to calculate the viscous supersonic flow over conical shapes at large angles of attack, with application to cones and delta wings. In the first approach the flow is assumed to be conical and the governing equations are solved at a given Reynolds number with a time-marching explicit finite-difference algorithm. In the second method the parabolized Navier-Stokes equations are solved with a space-marching implicit noniterative finite-difference algorithm. This latter approach is not restricted to conical shapes and provides a large improvement in computational efficiency over published methods. Results from the two procedures agree very well with each other and with available experimental data.

Vigneron, Y. C.↗
NASA NTRS1978

Calculation of supersonic viscous flow over delta wings with sharp subsonic leading edges

Two complementary procedures have been developed to calculate the viscous supersonic flow over conical shapes at large angles of attack, with application to cones and delta wings. In the first approach the flow is assumed to be conical and the governing equations are solved at a given Reynolds number with a time-marching explicit finite-difference algorithm. In the second method the parabolized Navier-Stokes equations are solved with a space-marching implicit noniterative finite-difference algorithm. This latter approach is not restricted to conical shapes and provides a large improvement in computational efficiency over published methods. Results from the two procedures agree very well with each other and with available experimental data.

Vigneron, Y. C.↗