Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “linear implicitness”

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 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
NASA NTRS1999

An O(Nm(sup 2)) Plane Solver for the Compressible Navier-Stokes Equations

A hierarchical multigrid algorithm for efficient steady solutions to the two-dimensional compressible Navier-Stokes equations is developed and demonstrated. The algorithm applies multigrid in two ways: a Full Approximation Scheme (FAS) for a nonlinear residual equation and a Correction Scheme (CS) for a linearized defect correction implicit equation. Multigrid analyses which include the effect of boundary conditions in one direction are used to estimate the convergence rate of the algorithm for a model convection equation. Three alternating-line- implicit algorithms are compared in terms of efficiency. The analyses indicate that full multigrid efficiency is not attained in the general case; the number of cycles to attain convergence is dependent on the mesh density for high-frequency cross-stream variations. However, the dependence is reasonably small and fast convergence is eventually attained for any given frequency with either the FAS or the CS scheme alone. The paper summarizes numerical computations for which convergence has been attained to within truncation error in a few multigrid cycles for both inviscid and viscous ow simulations on highly stretched meshes.

Thomas, J. L.↗
NASA NTRS1981

Stable boundary approximations for a class of implicit schemes for the one-dimensional inviscid equations of gas dynamics

The applicability to practical calculations of recent theoretical developments in the stability analysis of difference approximations for initial-boundary-value problems of the hyperbolic type. For the numerical experiments, select the one-dimensional inviscid gas-dynamic equations in conservation-law form is selected. A class of implicit schemes based on linear multistep methods for ordinary differential equations is chosen and the use of space or space-time extrapolations as implicit or explicit boundary schemes is emphasized. Some numerical examples with various inflow-outflow conditions highlight the commonly discussed issues: explicit versus implicit boundary schemes, unconditionally stable schemes, and underspecification or overspecification of boundary conditions.

Yee, H. C.↗
NASA NTRS1999

Numerical Solution of Incompressible Navier-Stokes Equations Using a Fractional-Step Approach

A fractional step method for the solution of steady and unsteady incompressible Navier-Stokes equations is outlined. The method is based on a finite volume formulation and uses the pressure in the cell center and the mass fluxes across the faces of each cell as dependent variables. Implicit treatment of convective and viscous terms in the momentum equations enables the numerical stability restrictions to be relaxed. The linearization error in the implicit solution of momentum equations is reduced by using three subiterations in order to achieve second order temporal accuracy for time-accurate calculations. In spatial discretizations of the momentum equations, a high-order (3rd and 5th) flux-difference splitting for the convective terms and a second-order central difference for the viscous terms are used. The resulting algebraic equations are solved with a line-relaxation scheme which allows the use of large time step. A four color ZEBRA scheme is employed after the line-relaxation procedure in the solution of the Poisson equation for pressure. This procedure is applied to a Couette flow problem using a distorted computational grid to show that the method minimizes grid effects. Additional benchmark cases include the unsteady laminar flow over a circular cylinder for Reynolds Numbers of 200, and a 3-D, steady, turbulent wingtip vortex wake propagation study. The solution algorithm does a very good job in resolving the vortex core when 5th-order upwind differencing and a modified production term in the Baldwin-Barth one-equation turbulence model are used with adequate grid resolution.

Kiris, Cetin↗
NASA NTRS1979

Generation of linear dynamic models from a digital nonlinear simulation

The results and methodology used to derive linear models from a nonlinear simulation are presented. It is shown that averaged positive and negative perturbations in the state variables can reduce numerical errors in finite difference, partial derivative approximations and, in the control inputs, can better approximate the system response in both directions about the operating point. Both explicit and implicit formulations are addressed. Linear models are derived for the F 100 engine, and comparisons of transients are made with the nonlinear simulation. The problem of startup transients in the nonlinear simulation in making these comparisons is addressed. Also, reduction of the linear models is investigated using the modal and normal techniques. Reduced-order models of the F 100 are derived and compared with the full-state models.

Daniele, C. J.↗
DOE OSTI2020

Approximate inverse-based block preconditioners in poroelasticity

We focus on the fully implicit solution of the linear systems arising from a three-field mixed finite element approximation of Biot’s poroleasticity equations. The objective is to develop algebraic block preconditioners for the efficient solution of such systems by Krylov subspace methods. In this work, we investigate the use of approximate inverse-based techniques to decouple the native system of equations and obtain explicit sparse approximations of the Schur complements related to the physics-based partitioning of the unknowns by field type. Here, the proposed methods are tested in various numerical experiments including real-world applications dealing with petroleum and geotechnical engineering.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2026

An implicit-explicit time splitting strategy for the far SOL plasma fluid model with DG-FEM discretization

We consider a far scrape-off layer (SOL) plasma fluid model of ions that is governed by a Braginskiitype model: a one-dimensional, nonlinear system of advection-diffusion equations coupled with a diffusion equation for neutral particles. Our motivation for studying this system arises from the coupling between the edge plasma and radio-frequency (RF) heating, where solving a far SOL plasma fluid model provides critical insights into edge plasma dynamics. Numerical simulations of plasma fluid models require advanced computational techniques to achieve both efficiency and accuracy, especially when resolving the boundary layer in magnetically confined plasmas. In this work, we propose an implicit-explicit time operator splitting strategy that allows for an efficient solution algorithm, where the diffusive terms are treated semi-implicitly requiring only a linear solve, while the advection part is handled explicitly using a strong-stability-preserving Runge-Kutta (SSP-RK3) scheme. This leads to a fully decoupled system in which the diffusion and advection sub-problems can be solved separately, simplifying the overall solution procedure and allowing for efficient parallelization, which is particularly relevant for exploring the impact of RF heating on the SOL plasma. The main challenge of the discretization is due to the strong coupling between diffusion and advection, particularly through the boundary conditions. This makes implementation of such a scheme in an accurate and stable manner nontrivial. We discuss in detail how to split the equations and manage boundary conditions to maintain stability and well-posedness for each subsystem. We also describe a spatial discretization approach, based on the discontinuous Galerkin finite element method (DG-FEM) and present numerical results for a one-dimensional system.

Burkovska, Olena [ORNL] (ORCID:0000000163101130)↗
NASA NTRS1990

Preconditioned conjugate gradient methods for the compressible Navier-Stokes equations

The compressible Navier-Stokes equations are solved for a variety of two-dimensional inviscid and viscous problems by preconditioned conjugate gradient-like algorithms. Roe's flux difference splitting technique is used to discretize the inviscid fluxes. The viscous terms are discretized by using central differences. An algebraic turbulence model is also incorporated. The system of linear equations which arises out of the linearization of a fully implicit scheme is solved iteratively by the well known methods of GMRES (Generalized Minimum Residual technique) and Chebyschev iteration. Incomplete LU factorization and block diagonal factorization are used as preconditioners. The resulting algorithm is competitive with the best current schemes, but has wide applications in parallel computing and unstructured mesh computations.

Venkatakrishnan, V.↗
NASA NTRSDate not supplied

Improvements in Iterative Convergence of FUN3D Solutions

This paper presents a hierarchical adaptive nonlinear iteration method (HANIM) implemented in NASA computational fluid dynamics code, FUN3D, to improve robustness and computational efficiency of FUN3Dsolutions. In contrast to the baseline iterative solver that relies on an approximate Jacobian, a simple multicolor Gauss-Seidel point-implicit iteration scheme, and linear CFL ramping, HANIM is based upon a hierarchy of modules including pre conditioner, generalized conjugate residual, realizability check, nonlinear control,and CFL adaption modules. HANIM performance is systematically compared with the performance of the baseline solver. The iterative solutions are compared for three aerodynamic benchmark cases: a subsonic separated flow around a hemisphere cylinder, a supersonic flow through a long duct, and a subsonic flow over the NASA wing-body juncture model. Two Reynolds-averaged Navier-Stokes turbulence models are used in these computations, namely, the negative variant of the linear one-equation Spalart-Allmar as model and its nonlinear extension based on quadratic constitutive relations.

Li Wang↗
NASA NTRSDate not supplied

Improvements in Iterative Convergence of FUN3D Solutions

This paper presents a hierarchical adaptive nonlinear iteration method (HANIM) implemented in the NASA computational fluid dynamics code, FUN3D, to improve robustness and computational efficiency. In contrast to the legacy FUN3D iterative solver that relies on an approximate Jacobian, a simple multicolor Gauss-Seidel point-implicit iteration scheme, and linear Courant-Friedrichs-Lewy number (CFL) ramping, HANIM is based upon a hierarchy of modules including preconditioner, generalized conjugate residual, realizability check, nonlinear control, and CFL adaption modules. HANIM performance is systematically compared with the performance of the legacy solver of FUN3D and a baseline solver based on a preconditioner alone. Iterative solutions are compared for three benchmark cases: a subsonic separated flow around a hemisphere cylinder, a supersonic flow through a long duct, and a subsonic flow over the NASA wing-fuselage juncture model. Two Reynolds-averaged Navier-Stokes turbulence models are used in these computations, namely, the negative variant of the linear one-equation Spalart-Allmaras model and its nonlinear extension based on quadratic constitutive relations.

CFD↗
NASA NTRS1986

Numerical experiments with a symmetric high-resolution shock-capturing scheme

Characteristic-based explicit and implicit total variation diminishing (TVD) schemes for the two-dimensional compressible Euler equations have recently been developed. This is a generalization of recent work of Roe and Davis to a wider class of symmetric (non-upwind) TVD schemes other than Lax-Wendroff. The Roe and Davis schemes can be viewed as a subset of the class of explicit methods. The main properties of the present class of schemes are that they can be implicit, and, when steady-state calculations are sought, the numerical solution is independent of the time step. In a recent paper, a comparison of a linearized form of the present implicit symmetric TVD scheme with an implicit upwind TVD scheme originally developed by Harten and modified by Yee was given. Results favored the symmetric method. It was found that the latter is just as accurate as the upwind method while requiring less computational effort. Currently, more numerical experiments are being conducted on time-accurate calculations and on the effect of grid topology, numerical boundary condition procedures, and different flow conditions on the behavior of the method for steady-state applications. The purpose here is to report experiences with this type of scheme and give guidelines for its use.

Yee, H. C.↗
NASA NTRS2001

The Use of Non-Standard Devices in Finite Element Analysis

A general mathematical description of the response behavior of thin-skin pneumatic envelopes and many other membrane and cable structures produces under-constrained systems that pose severe difficulties to analysis. These systems are mobile, and the general mathematical description exposes the mobility. Yet the response behavior of special under-constrained structures under special loadings can be accurately predicted using a constrained mathematical description. The static response behavior of systems that are infinitesimally mobile, such as a non-slack membrane subtended from a rigid or elastic boundary frame, can be easily analyzed using such general mathematical description as afforded by the non-linear, finite element method using an implicit solution scheme if the incremental uploading is guided through a suitable path. Similarly, if such structures are assembled with structural lack of fit that provides suitable self-stress, then dynamic response behavior can be predicted by the non-linear, finite element method and an implicit solution scheme. An explicit solution scheme is available for evolution problems. Such scheme can be used via the method of dynamic relaxation to obtain the solution to a static problem. In some sense, pneumatic envelopes and many other compliant structures can be said to have destiny under a specified loading system. What that means to the analyst is that what happens on the evolution path of the solution is irrelevant as long as equilibrium is achieved at destiny under full load and that the equilibrium is stable in the vicinity of that load. The purpose of this paper is to alert practitioners to the fact that non-standard procedures in finite element analysis are useful and can be legitimate although they burden their users with the requirement to use special caution. Some interesting findings that are useful to the US Scientific Balloon Program and that could not be obtained without non-standard techniques are presented.

Schur, Willi W.↗
NASA NTRS2016

An Optimized Multicolor Point-Implicit Solver for Unstructured Grid Applications on Graphics Processing Units

In the field of computational fluid dynamics, the Navier-Stokes equations are often solved using an unstructuredgrid approach to accommodate geometric complexity. Implicit solution methodologies for such spatial discretizations generally require frequent solution of large tightly-coupled systems of block-sparse linear equations. The multicolor point-implicit solver used in the current work typically requires a significant fraction of the overall application run time. In this work, an efficient implementation of the solver for graphics processing units is proposed. Several factors present unique challenges to achieving an efficient implementation in this environment. These include the variable amount of parallelism available in different kernel calls, indirect memory access patterns, low arithmetic intensity, and the requirement to support variable block sizes. In this work, the solver is reformulated to use standard sparse and dense Basic Linear Algebra Subprograms (BLAS) functions. However, numerical experiments show that the performance of the BLAS functions available in existing CUDA libraries is suboptimal for matrices representative of those encountered in actual simulations. Instead, optimized versions of these functions are developed. Depending on block size, the new implementations show performance gains of up to 7x over the existing CUDA library functions.

Zubair, Mohammad↗
NASA NTRS1989

A Computational Fluid Dynamics Algorithm on a Massively Parallel Computer

The discipline of computational fluid dynamics is demanding ever-increasing computational power to deal with complex fluid flow problems. We investigate the performance of a finite-difference computational fluid dynamics algorithm on a massively parallel computer, the Connection Machine. Of special interest is an implicit time-stepping algorithm; to obtain maximum performance from the Connection Machine, it is necessary to use a nonstandard algorithm to solve the linear systems that arise in the implicit algorithm. We find that the Connection Machine ran achieve very high computation rates on both explicit and implicit algorithms. The performance of the Connection Machine puts it in the same class as today's most powerful conventional supercomputers.

Jespersen, Dennis C.↗
NASA NTRS1978

Non-linear effects on sound propagation in a variable area duct carrying high subsonic Mach number flows

The general one-dimensional non-linear equation for the acoustic velocity potential in a variable area duct carrying high subsonic Mach number flows is presented and solved numerically using an implicit finite difference scheme. For the linearized equation with no flow, the present scheme is compared with the exact solution and the fourth-order Runge-Kutta method with excellent agreement for dimensionless time periods. Non-linear solutions are more sensitive to Mach numbers and exciting amplitudes and less sensitive to exciting frequencies. In general, non-linear effects can be safely neglected for low Mach number flows but must be accounted for when high Mach number flows are encountered.

Lumsdaine, E.↗
NASA NTRS1979

Computations of unsteady transonic flow governed by the conservative full potential equation using an alternating direction implicit algorithm

A development was the time linearization of the density function. This linearization reduces the solution process from solving just a single equation. Two sample cases were computed. First, a one dimensional traveling shock wave was computed and compared with the analytic solution. Second, a two dimensional case was calculated for a flow field which resulted from a thickening and subsequently, thinning airfoil. The resulting flow field, which included a traveling shock wave, was compared to the flow field obtained from the low frequency, small disturbance, transonic equation.

Goorjian, P. M.↗