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At least 811 records · Page 45
All sourcesNASA NTRSDOE OSTI
NASA NTRS2014

First-Order Hyperbolic System Method for Time-Dependent Advection-Diffusion Problems

A time-dependent extension of the first-order hyperbolic system method for advection-diffusion problems is introduced. Diffusive/viscous terms are written and discretized as a hyperbolic system, which recovers the original equation in the steady state. The resulting scheme offers advantages over traditional schemes: a dramatic simplification in the discretization, high-order accuracy in the solution gradients, and orders-of-magnitude convergence acceleration. The hyperbolic advection-diffusion system is discretized by the second-order upwind residual-distribution scheme in a unified manner, and the system of implicit-residual-equations is solved by Newton's method over every physical time step. The numerical results are presented for linear and nonlinear advection-diffusion problems, demonstrating solutions and gradients produced to the same order of accuracy, with rapid convergence over each physical time step, typically less than five Newton iterations.

Mazaheri, Alireza↗
DOE OSTI2022

The Schwarz alternating method for transient solid dynamics

Abstract In our earlier work, we formulated the Schwarz alternating method as a means for concurrent multiscale coupling in finite deformation solid mechanics for quasi‐static problems. Herein, we advance this method for the study of transient dynamic multiscale solid mechanics problems where information is exchanged back and forth between small and large scales. The extension to dynamics relies on the notion of a global time stepper. Within each global time step, the subdomains are coupled by the standard Schwarz iterative process. Remarkably, each subdomain can use its own time step or even its own time integrator to advance its solution in time, provided that they synchronize at each global time step. We study the performance of the Schwarz method on several examples designed for this purpose. Our numerical experiments demonstrate that the method is capable of coupling regions with different mesh resolutions, different element types, and different time integration schemes (e.g., implicit and explicit), all without introducing any artifacts that afflict other coupling methods for transient dynamics. Finally, we apply the dynamic Schwarz alternating method to the simulation of a bolted joint subjected to dynamic loading, as a demonstration of the performance of the method in a realistic scenario.

Mota, Alejandro↗
NASA NTRS1992

Development of iterative techniques for the solution of unsteady compressible viscous flows

The development of efficient iterative solution methods for the numerical solution of two- and three-dimensional compressible Navier-Stokes equations is discussed. Iterative time marching methods have several advantages over classical multi-step explicit time marching schemes, and non-iterative implicit time marching schemes. Iterative schemes have better stability characteristics than non-iterative explicit and implicit schemes. In this work, another approach based on the classical conjugate gradient method, known as the Generalized Minimum Residual (GMRES) algorithm is investigated. The GMRES algorithm has been used in the past by a number of researchers for solving steady viscous and inviscid flow problems. Here, we investigate the suitability of this algorithm for solving the system of non-linear equations that arise in unsteady Navier-Stokes solvers at each time step.

Sankar, Lakshmi N.↗
NASA NTRS1985

Finite element algorithms for compressible flow computation on a supercomputer

Methods of applying computational fluid dynamics techniques to engineering problems are discussed. The linking factors between theoretical and applied research are the shape and weight functions which produce the Galerkin finite element schemes. The flow is unsteady, viscous, heat conducting and compressible, and steady-state flows are the asymptotic limit of unsteady flows. All flows are described by the time-averaged Navier-Stokes equations (NSE) with mass and energy conservation. Local curvilinear intrinsic coordinates are applied to discretize the NSE in arbitrary geometric domains. A modified weighted residuals approach defines the discrete analogs of the physical systems modeled and a general interpolants method is used to derive families of numerical models, both implicit and explicit, finite difference and finite elemnt, from a single point of departure. Time-dependent element approximations are achieved with a progressive assembly of generalized elements method. Hyperbolic steady-state Euler algorithms and quasi-parabolic are spatial marching algorithms for solving the discretized equations. Application of the techniques is illustrated through calculation of the compressible flow around a hypersonic flight vehicle at 100,000 ft at zero angle of attack at speeds of Mach 4-10.

Spradley, L. W.↗
NASA NTRS1989

LU-SGS implicit algorithm for three-dimensional incompressible Navier-Stokes equations with source term

A numerical method is developed for solving the incompressible Navier-Stokes equations using the concept of pseudocompressibility. A lower-upper symmetric-Gauss-Seidel implicit scheme is developed for three-dimensional incompressible viscous flow computations. The present algorithm offers additional advantages when solving the flow equations with source terms. Complete vectorizability of the algorithm on oblique planes of sweep in three-dimensions is accomplished in a new flow solver, INS3D-LU code. Spatial differencing is a second-order accurate semi-discrete finite-volume method augmented by a third-order accurate numerical dissipation model which is based on spectral-radii. Comparison of numerical solutions for a curved duct with experimental data shows good agreement. The method is applied to calculate the inducer flow of the Space Shuttle Main Engine turbopump.

Yoon, Seokkwan↗
NASA NTRS1995

Calculation of three-dimensional (3-D) internal flow by means of the velocity-vorticity formulation on a staggered grid

A method has been developed to accurately compute the viscous flow in three-dimensional (3-D) enclosures. This method is the 3-D extension of a two-dimensional (2-D) method developed for the calculation of flow over airfoils. The 2-D method has been tested extensively and has been shown to accurately reproduce experimental results. As in the 2-D method, the 3-D method provides for the non-iterative 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 methodology. In the staggered grid method, the three components of vorticity are defined at the centers of the computational cell sides, while the velocity components are defined as normal vectors at the centers of the computational cell faces. The staggered grid orientation provides for the accurate definition of the vorticity components at the vorticity locations, the divergence of vorticity at the mesh cell nodes and the conservation of mass at the mesh cell centers. The solution is obtained by utilizing a fractional step solution technique in the three coordinate directions. The boundary conditions for the vorticity and velocity are calculated implicitly as part of the solution. The method provides for the non-iterative solution of the flow field and satisfies the conservation of mass and divergence of vorticity to machine zero at each time step. To test the method, the calculation of simple driven cavity flows have been computed. The driven cavity flow is defined as the flow in an enclosure driven by a moving upper plate at the top of the enclosure. To demonstrate the ability of the method to predict the flow in arbitrary cavities, results will he shown for both cubic and curved cavities.

Stremel, Paul M.↗
DOE OSTI2025

Sylvester-preconditioned adaptive-rank implicit time integrators for advection-diffusion equations with variable coefficients

Here, we consider the adaptive-rank integration of multi-dimensional time-dependent advection-diffusion partial differential equations (PDEs) with variable coefficients. We employ a standard finite-difference method for spatial discretization coupled with high-order diagonally implicit Runge-Kutta temporal schemes. The discrete equation is a generalized Sylvester equation (GSE), which we solve with a projection-based adaptive-rank algorithm structured around two key strategies: (i) constructing dimension-wise subspaces using a novel atypical extended Krylov strategy, and (ii) efficiently solving the basis coefficient matrix with a preconditioned GMRES solver. The low-rank decomposition is performed in 2D using SVD and with high-order SVD (HOSVD) in 3D to represent the tensor in a compressed Tucker format. For d-dimensional problems (here, d = 2 or 3), the computational complexity and memory storage of the approach are found numerically to scale as and $\mathscr{O}(Nr^2) + \mathscr{O} (r^{d+1})$ and $\mathscr{O}(Nr) + \mathscr{O} (r^{d})$, respectively, with the one-dimensional resolution and the maximal rank during the Krylov iteration (which we find to be largely independent of on our numerical examples). We present numerical examples that illustrate the advertised properties of the algorithm.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1993

Prediction of static performance for single expansion ramp nozzles

A multiblock three-dimensional Navier-Stokes method was utilized in a two-dimensional fully implicit mode to calculate the flowfield of a single expansion ramp nozzle configuration. The code has been shown previously to be fairly accurate in predicting three-dimensional nozzle flowfields and internal performance for several axisymmetric and nonaxisymmetric geometries. A two-dimensional implementation of the method was used to reduce the resources required to obtain preliminary performance parameters of nozzle concepts. A two-dimensional description of a single-expansion ramp nozzle configuration was analyzed to verify the applicability of the Navier-Stokes code and nozzle performance package to this class of nozzles. Internal static pressure distributions, discharge coefficient and thrust ratio quantities were calculated for a range of operating conditions. Comparisons of predicted performance parameters with experimental data were within 0.5 percent for mass flow, and typically within l.5 percent for thrust ratio.

Carlson, John R.↗
NASA NTRS1983

Monotone implicit algorithms for the small-disturbance and full potential equations applied to transonic flows

Numerical calculations of transonic flows by potential equations typically use algorithms that change the method of calculation for regions of subsonic and supersonic flow. In this paper, implicit approximate-factorization algorithms are modified to use the monotonic switch in the type of finite-differencing that was developed by Godunov for the Euler equations. Calculations of flows over airfoils by these algorithms are compared with calculations by other methods that are in common usage. For the small-disturbance potential equation, comparisons are made with the Murman-Cole method and the monotone method of Engquist and Osher for both steady and unsteady flows. For the full potential equation, comparisons are made with the methods of Jameson and of Holst and Ballhaus for steady flows. The comparisons show that the monotone methods are more stable. For steady flows, solutions are obtained for cases where the Murman-Cole switch requires a time step over ten times smaller in order for the calculations to remain stable. These improvements are achieved with no increase in computer storage and only minor modifications in current codes.

Goorjian, P. M.↗
DOE OSTI2022

Numerical schemes for a multi-species BGK model with velocity-dependent collision frequency

Here, we consider a kinetic description of multi-species gas mixture modeled with Bhatnagar-Gross-Krook (BGK) collision operators, in which the collision frequency varies not only in time and space but also with the microscopic velocity. In this model, the Maxwellians typically used in standard BGK operators are replaced by a generalization of such target functions, which are defined by a variational procedure. In this paper we present a numerical method for simulating this model, which uses an Implicit-Explicit (IMEX) scheme to minimize a certain potential function, mimicking the Lagrange functional that appears in the theoretical derivation. We show that theoretical properties such as conservation of mass, total momentum and total energy as well as positivity of the distribution functions are preserved by the numerical method, and illustrate its usefulness and effectiveness with numerical examples.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

A sharp immersed method for 2D flow-body interactions using the vorticity-velocity Navier-Stokes equations

Immersed methods discretize boundary conditions for complex geometries on background Cartesian grids. Here, this makes such methods especially suitable for two-way coupled flow-body problems, where the body mechanics are partially driven by hydrodynamic forces. However, for the vorticity-velocity form of the Navier-Stokes equations, existing immersed geometry discretizations for two-way coupled problems only achieve first order spatial accuracy near solid boundaries. Here we introduce a sharp-interface approach based on the immersed interface method to handle the one- and two-way coupling between an incompressible flow and one or more rigid bodies using the 2D vorticity-velocity Navier-Stokes equations. Our main contributions are three-fold. First, we develop and analyze a moving boundary treatment for sharp immersed methods that can be applied to PDEs with implicitly defined boundary conditions, such as those commonly imposed on the vorticity field. Second, we develop a two-way coupling methodology for the vorticity-velocity Navier-Stokes equations based on control-volume momentum balance that does not require the pressure field. Third, we show through extensive testing and validation that our resulting flow-body solver reaches second-order accuracy for most practical scenarios, and provides significant efficiency benefits compared to a representative first-order approach.

42 ENGINEERING↗
NASA NTRS1989

Unsteady aerodynamic simulation of multiple bodies in relative motion

A prototype method for time-accurate simulation of multiple aerodynamic bodies in relative motion is presented. The method is general and features unsteady chimera domain decomposition techniques and an implicit approximately factored finite-difference procedure to solve the time-dependent thin-layer Navier-Stokes equations. The method is applied to a set of two- and three-dimensional test problems to establish spatial and temporal accuracy, quantify computational efficiency, and begin to test overall code robustness.

Meakin, Robert L.↗
NASA NTRS1989

Unsteady aerodynamic simulation of multiple bodies in relative motion: A prototype method

A prototype method for time-accurate simulation of multiple aerodynamic bodies in relative motion is presented. The method is general and features unsteady chimera domain decomposition techniques and an implicit approximately factored finite-difference procedure to solve the time-dependent thin-layer Navier-Stokes equations. The method is applied to a set of two- and three- dimensional test problems to establish spatial and temporal accuracy, quantify computational efficiency, and begin to test overall code robustness.

Meakin, Robert L.↗
NASA NTRS1989

An efficient cell-vertex multigrid scheme for the three-dimensional Navier-Stokes equations

A cell-vertex scheme for the three-dimensional Navier-Stokes equations, which is based on central difference approximations and Runge-Kutta time stepping, is described. Using local time stepping, implicit residual smoothing with locally varying coefficients, a multigrid method and carefully controlled dissipative terms, very good convergence rates are obtained for two- and three-dimensional flows. Details of the acceleration techniques, which are important for convergence on meshes with high aspect-ratio cells, are discussed. Emphasis is put on the analysis of the stability properties of the implicit smoothing of the explicit residuals with coefficients, which depend on cell aspect ratios.

Radespiel, R.↗
DOE OSTI2020

A Hybrid Lagrangian/Eulerian Collocated Velocity Advection and Projection Method for Fluid Simulation

Abstract We present a hybrid particle/grid approach for simulating incompressible fluids on collocated velocity grids. Our approach supports both particle‐based Lagrangian advection in very detailed regions of the flow and efficient Eulerian grid‐based advection in other regions of the flow. A novel Backward Semi‐Lagrangian method is derived to improve accuracy of grid based advection. Our approach utilizes the implicit formula associated with solutions of the inviscid Burgers’ equation. We solve this equation using Newton's method enabled by C 1 continuous grid interpolation. We enforce incompressibility over collocated, rather than staggered grids. Our projection technique is variational and designed for B‐spline interpolation over regular grids where multiquadratic interpolation is used for velocity and multilinear interpolation for pressure. Despite our use of regular grids, we extend the variational technique to allow for cut‐cell definition of irregular flow domains for both Dirichlet and free surface boundary conditions.

Gagniere, S.↗
NASA NTRS1993

Multigrid methods for flow transition in three-dimensional boundary layers with surface roughness

The efficient multilevel adaptive method has been successfully applied to perform direct numerical simulations (DNS) of flow transition in 3-D channels and 3-D boundary layers with 2-D and 3-D isolated and distributed roughness in a curvilinear coordinate system. A fourth-order finite difference technique on stretched and staggered grids, a fully-implicit time marching scheme, a semi-coarsening multigrid method associated with line distributive relaxation scheme, and an improved outflow boundary-condition treatment, which needs only a very short buffer domain to damp all order-one wave reflections, are developed. These approaches make the multigrid DNS code very accurate and efficient. This allows us not only to be able to do spatial DNS for the 3-D channel and flat plate at low computational costs, but also to do spatial DNS for transition in the 3-D boundary layer with 3-D single and multiple roughness elements, which would have extremely high computational costs with conventional methods. Numerical results show good agreement with the linear stability theory, the secondary instability theory, and a number of laboratory experiments. The contribution of isolated and distributed roughness to transition is analyzed.

Liu, Chaoqun↗
NASA NTRS1993

Line relaxation methods for the solution of 2D and 3D compressible flows

An implicit finite element based algorithm for the compressible Navier-Stokes equations is outlined, and the solution of the resulting equation by a line relaxation on general meshes of triangles or tetrahedra is described. The problem of generating and adapting unstructured meshes for viscous flows is reexamined, and an approach for both 2D and 3D simulations is proposed. An efficient approach appears to be the use of an implicit/explicit procedure, with the implicit treatment being restricted to those regions of the mesh where viscous effects are known to be dominant. Numerical examples demonstrating the computational performance of the proposed techniques are given.

Hassan, O.↗