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Results for “semi-implicit scheme”

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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28 records · Page 2
All sourcesNASA NTRSDOE OSTI
NASA NTRS1986

A relaxation technique for the parabolized Navier-Stokes (PNS) equations

A rapidly converging relaxation technique for the parabolized Navier-Stokes equations has been devised. The scheme is applicable in both supersonic and subsonic flows, but it is discussed here in the context of supersonic flows. The upstream propagating acoustic influence in the subsonic part of the flow is introduced semi-implicitly through the streamwise momentum equation applied on the body, and through a forward-differencing on the streamwise pressure gradient term in the interior. This procedure yields a new boundary condition on the energy in the total energy equation. The pressure-velocity system in the subsonic layer is coupled, but the positive time-like marching characteristic of the governing equations is still maintained. The relaxation technique is demontrated to work for a three-dimensional flow over a cone-flare in supersonic flight.

Kaul, Upender K.↗
NASA NTRS1987

Studies of pressure-velocity coupling schemes for analysis of incompressible and compressible flows

Two pressure-velocity coupling schemes, both of which solve the fully implicit discretized equations governing the flow of fluids were examined, and the capability of performing large Reynolds number, low Mach number compressible flow calculations were assessed. The semi-implicit iterative SIMPLE algorithm is extended to handle transient compressible flow calculations. This extension takes into account a strong coupling between the pressure and temperature through a correction procedure, based on the equations of state. Results obtained from the extended SIMPLE algorithm are then compared to similar results obtained from the non-iterative PISO algorithm. Both time-dependent and steady state calculations were performed using an axisymmetric 2:1 pipe expansion geometry and laminar flow conditions corresponding to Reynolds number of 1000 and Mach number of 2.0. For calculations simulating a time-dependent compression/expansion process, both schemes exhibit transient features in excellent agreement with each other, and moreover, the PISO method shows a significant computational time reduction of 60 percent over the SIMPLE scheme, regardless of the time step size or grid size employed. The effects of numerical diffusion are shown to be significant in these calculations. For steady state compressible flows, however, the SIMPLE algorithm displays increasing computational efficiency over the PISO method as the time step sizes employed to reach steady state conditions are decreased.

Burgreen, Gregory Wayne↗
NASA NTRS1987

Extension of a semi-implicit shock-capturing algorithm for 3-D fully coupled, chemically reacting flows in generalized coordinates

A semiimplicit high-resolution shock-capturing method for multidimensional systems of hyperbolic conservation laws with stiff source terms has been developed by Yee and Shinn (1987). The goal of this work is to extend this method to solve the three-dimensional fully coupled Navier-Stokes equations for a hypersonic chemically reacting flow in generalized coordinates. In this formulation, the global continuity equation was replaced by all the species continuity equations. The shock-capturing technique is a second-order-accurate, symmetric total-variation-diminishing method which accounts fully and directly for the coupling among the fluid and all the species. To verify the current approach, it was implemented into an existing computer code which contained the MacCormack method. Test results for a five-species reacting flow are shown to be oscillation-free around the shock, and the time spent per iteration only doubles when compared to the result using classical way of supplying numerical dissipation. The extra computation is more than justified by the elimination of spurious oscillation and nonlinear instability associated with the classical shock-capturing schemes in computing hypersonic reacting flows.

Shinn, J. L.↗
NASA NTRS1980

Numerical solution techniques for unsteady transonic aerodynamics problems

Basic concepts of finite difference solution techniques for unsteady transonic flows are presented. The hierarchy of mathematical forumulations that approximate the Navier-Stokes equations are reviewed. The basic concepts involved in constructing numerical algorthms to solve these formulations are given. Semi-implicit and implicit schemes are constructed and analyzed. The discussion focuses primarily on techniques for solving the low frequency transonic small disturbance equation. This is the simplest formulation that contains the essence of inviscid unsteady transonic flow physics. The low frequency formulation is emphasized here because codes based on this theory can be run in minutes of processor time on currently available computers. Furthermore, numerical techniques involved in solving this simple formulation also apply to the more complicated formulations. Extensions to these formulations are briefly described. An indication of the present capability for solving unsteady transonic flows is provided. Important areas of future research for the advancement of computational unsteady transonic aerodynamics are described.

Ballhaus, W. F.↗
NASA NTRS1981

Multigrid simulation of asymptotic curved-duct flows using a semi-implicit numerical technique

Asymptotic flows inside curved ducts of rectangular as well as polar cross section are analyzed using the Navier-Stokes equations in terms of the axial velocity and vorticity and the cross-flow stream function. Numerical solutions of the three second-order coupled elliptic partial differential equations governing this flow are obtained efficiently using the coupled alternating-direction implicit (ADI) method as well as the multigrid strongly-implicit (SI) scheme. For the flow configuration studied, the ADI method is found to be more sensitive to the time steps used than is the SI scheme. Use of the multigrid-coupled-strongly-implicit (MG-SI) scheme makes it possible to efficiently obtain fine-grid solutions for configurations having strong secondary flow. It is shown that, for this asymptotic curved-duct flow, the similarity parameter of significance is the Dean's number K rather than the Reynolds number Re. Results are obtained for curved ducts with square cross sections for K up to 900, which here corresponds to Re = 9,000 for this internal flow configuration.

Ghia, K. N.↗
NASA NTRS1986

The efficient calculation of chemically reacting flow

A semi-implicit finite volume formulation is used to study flows with chemical reactions. In this formulation the source terms resulting from the chemical reactions are treated implicitly and the resulting system of partial differential equations is solved using two time-stepping schemes. The first is based on the Runge-Kutta method while the second is based on an Adams predictor-corrector method. Results show that improvements in computational efficiency depend to a large extent on the manner in which the source term is treated. Further, analysis and computation indicate that the Runge-Kutta method is more efficient than the Adams methods. Finally, an adaptive time stepping scheme is developed to study problems involving shock ignition. Calculations for a hydrogen-air system agree well with other methods.

Eklund, D. R.↗
NASA NTRS1986

Semi-implicit and fully implicit shock-capturing methods for hyperbolic conservation laws with stiff source terms

Some numerical aspects of finite-difference algorithms for nonlinear multidimensional hyperbolic conservation laws with stiff nonhomogenous (source) terms are discussed. If the stiffness is entirely dominated by the source term, a semi-implicit shock-capturing method is proposed provided that the Jacobian of the soruce terms possesses certain properties. The proposed semi-implicit method can be viewed as a variant of the Bussing and Murman point-implicit scheme with a more appropriate numerical dissipation for the computation of strong shock waves. However, if the stiffness is not solely dominated by the source terms, a fully implicit method would be a better choice. The situation is complicated by problems that are higher than one dimension, and the presence of stiff source terms further complicates the solution procedures for alternating direction implicit (ADI) methods. Several alternatives are discussed. The primary motivation for constructing these schemes was to address thermally and chemically nonequilibrium flows in the hypersonic regime. Due to the unique structure of the eigenvalues and eigenvectors for fluid flows of this type, the computation can be simplified, thus providing a more efficient solution procedure than one might have anticipated.

Yee, H. C.↗
NASA NTRS1987

Semi-implicit and fully implicit shock-capturing methods for hyperbolic conservation laws with stiff source terms

Some numerical aspects of finite-difference algorithms for nonlinear multidimensional hyperbolic conservation laws with stiff nonhomogeneous (source) terms are discussed. If the stiffness is entirely dominated by the source term, a semi-implicit shock-capturing method is proposed provided that the Jacobian of the source terms possesses certain properties. The proposed semi-implicit method can be viewed as a variant of the Bussing and Murman point-implicit scheme with a more appropriate numerical dissipation for the computation of strong shock waves. However, if the stiffness is not solely dominated by the source terms, a fully implicit method would be a better choice. The situation is complicated by problems that are higher than one dimension, and the presence of stiff source terms further complicates the solution procedures for alternating direction implicit (ADI) methods. Several alternatives are discussed. The primary motivation for constructing these schemes was to address thermally and chemically nonequilibrium flows in the hypersonic regime. Due to the unique structure of the eigenvalues and eigenvectors for fluid flows of this type, the computation can be simplified, thus providing a more efficient solution procedure than one might have anticipated.

Yee, H. C.↗
NASA NTRS1993

Variational data assimilation with a semi-Lagrangian semi-implicit global shallow-water equation model and its adjoint

An adjoint model is developed for variational data assimilation using the 2D semi-Lagrangian semi-implicit (SLSI) shallow-water equation global model of Bates et al. with special attention being paid to the linearization of the interpolation routines. It is demonstrated that with larger time steps the limit of the validity of the tangent linear model will be curtailed due to the interpolations, especially in regions where sharp gradients in the interpolated variables coupled with strong advective wind occur, a synoptic situation common in the high latitudes. This effect is particularly evident near the pole in the Northern Hemisphere during the winter season. Variational data assimilation experiments of 'identical twin' type with observations available only at the end of the assimilation period perform well with this adjoint model. It is confirmed that the computational efficiency of the semi-Lagrangian scheme is preserved during the minimization process, related to the variational data assimilation procedure.

Li, Y.↗
NASA NTRS2010

Adaptive Numerical Algorithms in Space Weather Modeling

Space weather describes the various processes in the Sun-Earth system that present danger to human health and technology. The goal of space weather forecasting is to provide an opportunity to mitigate these negative effects. Physics-based space weather modeling is characterized by disparate temporal and spatial scales as well as by different physics in different domains. A multi-physics system can be modeled by a software framework comprising of several components. Each component corresponds to a physics domain, and each component is represented by one or more numerical models. The publicly available Space Weather Modeling Framework (SWMF) can execute and couple together several components distributed over a parallel machine in a flexible and efficient manner. The framework also allows resolving disparate spatial and temporal scales with independent spatial and temporal discretizations in the various models. Several of the computationally most expensive domains of the framework are modeled by the Block-Adaptive Tree Solar wind Roe Upwind Scheme (BATS-R-US) code that can solve various forms of the magnetohydrodynamics (MHD) equations, including Hall, semi-relativistic, multi-species and multi-fluid MHD, anisotropic pressure, radiative transport and heat conduction. Modeling disparate scales within BATS-R-US is achieved by a block-adaptive mesh both in Cartesian and generalized coordinates. Most recently we have created a new core for BATS-R-US: the Block-Adaptive Tree Library (BATL) that provides a general toolkit for creating, load balancing and message passing in a 1, 2 or 3 dimensional block-adaptive grid. We describe the algorithms of BATL and demonstrate its efficiency and scaling properties for various problems. BATS-R-US uses several time-integration schemes to address multiple time-scales: explicit time stepping with fixed or local time steps, partially steady-state evolution, point-implicit, semi-implicit, explicit/implicit, and fully implicit numerical schemes. Depending on the application, we find that different time stepping methods are optimal. Several of the time integration schemes exploit the block-based granularity of the grid structure. The framework and the adaptive algorithms enable physics based space weather modeling and even forecasting.

Toth, Gabor↗