Results for “solver” — Page 5

NASA NTRSDate not supplied

Edge-Based Viscous Method for Mixed-Element Node-Centered Finite-Volume Solvers

A novel, efficient, edge-based viscous (EBV) discretization method has been recently developed, implemented in a practical, unstructured-grid, node-centered, finite-volume flow solver, and applied to viscous-kernel computations that include evaluations of meanflow viscous fluxes, turbulence-model and chemistry-model diffusion terms, and the corresponding Jacobian contributions. Initially, the EBV method had been implemented for tetrahedral grids and demonstrated multifold acceleration of all viscous-kernel computations. This paper presents an extension of the EBV method for mixed-element grids. In addition to the primal edges of a given mixed-element grid, virtual edges are introduced to connect cell nodes that are not connected by a primal edge. The EBV method uses an efficient loop over all (primal and virtual) edges and features a compact discretization stencil based on the nearest neighbors. This study verifies the EBV method and assesses its efficiency on mixed-element grids by comparing the EBV solution accuracy and iterative convergence with those of well-established solutions obtained using a cell-based viscous (CBV) discretization method. The EBV solver’s memory footprint is optimized and often smaller than the memory footprint of the CBV solver. A multifold speedup is demonstrated for all viscous-kernel computations resulting in significant reduction of the time to solutions for several benchmark mixed-element-grid computations, including simulations of a flow around NASA’s juncture-flow model and a hypersonic, chemically reacting flow around a blunt body.

CFD↗

NASA NTRSDate not supplied

Edge-Based Viscous Method for Mixed-Element Node-Centered Finite-Volume Solvers

A novel, efficient, edge-based viscous (EBV) discretization method has been recently developed, implemented in a practical, unstructured-grid, node-centered, finite-volume flow solver, and applied to viscous-kernel computations that include evaluations of meanflow viscous fluxes, turbulence-model and chemistry-model diffusion terms, and the corresponding Jacobian contributions. Initially, the EBV method had been implemented for tetrahedral grids and demonstrated multifold acceleration of all viscous-kernel computations. This paper presents an extension of the EBV method for mixed-element grids. In addition to the primal edges of a given mixed-element grid, virtual edges are introduced to connect cell nodes that are not connected by a primal edge. The EBV method uses an efficient loop over all (primal and virtual) edges and features a compact discretization stencil based on the nearest neighbors. This study verifies the EBV method and assesses its efficiency on mixed-element grids by comparing the EBV solution accuracy and iterative convergence with those of well-established solutions obtained using a cell-based viscous (CBV) discretization method. The EBV solver’s memory footprint is optimized and often smaller than the memory footprint of the CBV solver. A multifold speedup is demonstrated for all viscous-kernel computations resulting in significant reduction of the time to solutions for several benchmark mixed-element-grid computations, including simulations of a flow around NASA’s juncture-flow model and a hypersonic, chemically reacting flow around a blunt body.

Edge-based viscous method↗

NASA NTRSDate not supplied

Computational Analysis of a Boundary-Layer Ingesting Tailcone Thruster Configuration Within the National Transonic Facility Using the LAVA Solver

Boundary-layer ingesting (BLI) propulsion systems are one of the many technologies currently under investigation within the aerospace community to meet NASA’s Advanced Air Transport Technology project goal of a sustainable future in aviation. To that end, an experimental campaign was conducted in the National Transonic Facility (NTF) to study the propulsion-airframe integration effects of the Boundary-Layer Ingesting Tailcone System installed in the aft portion of a 2.7% scale design of the NASA Common Research Model (CRM). This test was accompanied by a numerical simulation effort using the Launch, Ascent, and Vehicle Aerodynamics (LAVA) solver, to validate the applicability of current best-practice Reynolds-averaged Navier Stokes (RANS) models in accurately predicting the relevant flow-physics in free-air. A total of 205 steady RANS simulations were performed using LAVA, covering the range of conditions present in the NTF test matrix. Flow conditions ranged from 5- to 15-million Reynolds number, Mach numbers of 0.75, 0.80 and 0.85, and angles-of-attack between –3° and 4°. Four different mass-flow plugs were also tested to assess propulsor operating condition effects. Sensitivity to these flow conditions are analyzed in detail, especially in terms of the nacelle flow distortion which was the main subject of the study. Aerodynamic load coefficients, aftbody boundary-layer measurements and fuselage pressure tap results are also discussed, providing a wide range of validation results from this experimental campaign. This validation effort shows that current best-practices using RANS models within the LAVA solver flow solver are well suited for predicting the inlet flow distortion characteristics of novel aircraft configurations employing BLI at the aft end of the fuselage.

AATT↗

NASA NTRSDate not supplied

Implicit Preconditioning for Explicit Multigrid Solvers on Cut-Cell Cartesian Meshes

This work assesses the effectiveness of linearized implicit Euler preconditioning for multigrid solvers using an unpreconditioned, Jacobian-free Newton Krylov method to converge the linear system of equations. Multigrid convergence rates improve to approximately 0.75 across the cases tested including a Mach 2 supersonic wedge, transonic NACA 0012 airfoil, and ONERA M6 wing. While larger Krylov subspaces increase the convergence rate, they also increase the computational cost, such that 4-8 Krylov vectors often offers the fastest turnaround. Further reductions in computational cost are achieved with a sequential hybrid preconditioner that begins with the explicit multigrid solver before transitioning to the preconditioned algorithm later on. In addition, a novel implementation of dual time stepping is extended to include both common BDF methods as well as high-order implicit Runge-Kutta schemes. This particular formulation, which uses A −1 preconditioning, is amenable to matrix-free solvers, and the L-stable methods are especially suited for meshes with arbitrarily small cut-cells. Asymptotic order of convergence is demonstrated for BDF1, BDF2, SDIRK2, and 3rd-order Radau IIA time integration with unsteady 2D vortex simulations.

ARMD↗

NASA NTRSDate not supplied

Computational Analysis of a Boundary Layer Ingesting Tailcone Thruster Configuration Using the LAVA Curvilinear Solver

Boundary layer ingesting (BLI) propulsion systems are one of the many technologies currently under investigation within the aerospace community to meet NASA's Advanced Air Transport Technology project goal of a sustainable future in aviation. To that end, an experimental campaign was conducted in the National Transonic Facility (NTF) wind tunnel to study the propulsion-airframe integration effects of the Boundary Layer Ingesting Tailcone System installed in the aft portion of a 2.7% scale design of the NASA Common Research Model (CRM). This test was accompanied by a numerical simulation effort using the Launch, Ascent, and Vehicle Aerodynamics (LAVA) curvilinear solver to validate the applicability of current best-practice Reynolds-Averaged Navier-Stokes (RANS) models in accurately predicting the relevant flow physics in free-air. A total of 205 steady RANS simulations were performed using LAVA, covering the range of conditions present in the NTF test matrix. Flow conditions ranged from 5- to 15-million Reynolds number, Mach numbers of 0.75, 0.80 and 0.85, and angles of attack between -3 and 4 degrees. Four different mass-flow plugs were also tested to assess propulsor operating condition effects. Sensitivity to these flow conditions is analyzed in detail, especially in terms of the nacelle flow distortion which was the main subject of the study. Aerodynamic load coefficients, aft body boundary layer measurements and fuselage pressure tap results are also discussed, providing a wide range of validation results from this experimental campaign. This validation effort shows that current best-practices using RANS models within the LAVA curvilinear solver flow solver are well suited for predicting the inlet flow distortion characteristics of novel aircraft configurations employing BLI at the aft end of the fuselage. This talk will cover the combined experimental and numerical efforts that resulted from this BLI-focused investigation.

ARMD↗

NASA NTRS1977

Variants and extensions of a fast direct numerical cauchy-riemann solver, with illustrative applications

Revised and extended versions of a fast, direct (noniterative) numerical Cauchy-Riemann solver are presented for solving finite difference approximations of first order systems of partial differential equations. Although the difference operators treated are linear and elliptic, one significant application of these extended direct Cauchy-Riemann solvers is in the fast, semidirect (iterative) solution of fluid dynamic problems governed by the nonlinear mixed elliptic-hyperbolic equations of transonic flow. Different versions of the algorithms are derived and the corresponding FORTRAN computer programs for a simple example problem are described and listed. The algorithms are demonstrated to be efficient and accurate.

Martin, E. D.↗

NASA NTRS1977

MACSYMA's symbolic ordinary differential equation solver

The MACSYMA's symbolic ordinary differential equation solver ODE2 is described. The code for this routine is delineated, which is of interest because it is written in top-level MACSYMA language, and may serve as a good example of programming in that language. Other symbolic ordinary differential equation solvers are mentioned.

Golden, J. P.↗

NASA NTRS1977

Fast methods incorporating direct elliptic solvers for nonlinear applications in fluid dynamics

Semidirect methods are discussed, their present role, as well as some developments for their application in computational fluid dynamics. A semidirect method is a computational scheme that uses a fast, direct, elliptic solver as the driving algorithm for the iterative solution of finite difference equations. Specific subtopics include: (1) direct Cauchy Riemann solvers for first order elliptic equations; (2) application of the semidirect method to the mixed elliptic hyperbolic problem of steady, inviscid transonic flow; and (3) the treatment of interior conditions, such as those on an airfoil or wing, in semidirect methods.

Martin, E. D.↗

NASA NTRS1977

A block iterative LU solver for weakly coupled linear systems

A hybrid technique, called the block iterative LU solver, is proposed for solving the linear equations resulting from a finite element numerical analysis of certain fluid dynamics problems where the equations are weakly coupled between distinct sets of variables. Either the block Jacobi iterative method or the block Gauss-Seidel iterative solver is combined with LU decomposition.

Cooke, C. H.↗

NASA NTRS1987

Navier-Stokes cascade analysis with a stiff Kappa-Epsilon turbulence solver

The two dimensional, compressible, thin layer Navier-Stokes equations with the Baldwin-Lomax turbulence model and the kinetic energy-energy dissipation (k-epsilon) model are solved numerically to simulate the flow through a cascade. The governing equations are solved for the entire flow domain, without the boundary layer assumptions. The stiffness of the k-epsilon equations is discussed. A semi-implicit, Runge-Kutta, time-marching scheme is developed to solve the k-epsilon equations. The impact of the k-epsilon solver on the explicit Runge-Kutta Navier-Stokes solver is discussed. Numerical solutions are presented for two dimensional turbulent flow over a flat plate and a double circular arc cascade and compared with experimental data.

Liu, Jong-Shang↗

NASA NTRS1988

The development of an intelligent interface to a computational fluid dynamics flow-solver code

Researchers at NASA Lewis are currently developing an 'intelligent' interface to aid in the development and use of large, computational fluid dynamics flow-solver codes for studying the internal fluid behavior of aerospace propulsion systems. This paper discusses the requirements, design, and implementation of an intelligent interface to Proteus, a general purpose, 3-D, Navier-Stokes flow solver. The interface is called PROTAIS to denote its introduction of artificial intelligence (AI) concepts to the Proteus code.

Williams, Anthony D.↗

NASA NTRS1988

A point implicit unstructured grid solver for the Euler and Navier-Stokes equations

An upwind finite element technique that uses cell centered quantities and implicit and/or explicit time marching has been developed for computing hypersonic laminar viscous flows using adaptive unstructured triangular grids. A structured grid of quadrilaterals is laid out near the body surface. For inviscid flows the method is stable at Courant numbers of over 100,000. A first order basic scheme and a higher order flux corrected transport (FCT) scheme have been implemented. This technique has been applied to the problem of predicting type III and IV shock wave interactions on a cylinder, with a view of simulating the pressure and heating rate augmentation caused by an impinging shock on the leading edge of a cowl lip of an engine inlet. The predictions of wall pressure and heating rates compare very well with experimental data. The flow features are very distinctly captured with a sequence of adaptively generated grids. The adaptive mesh generator and the upwind Navier-Stokes solver are combined in a set of programs called LARCNESS, an acronym for Langley Adaptive Remeshing Code and Navier-Stokes Solver.

Thareja, Rajiv R.↗

NASA NTRS1988

Navier-Stokes cascade analysis with a stiff k-epsilon turbulence solver

The two dimensional, compressible, thin layer Navier-Stokes equations with the Baldwin-Lomax turbulence model and the kinetic energy-energy dissipation (k-epsilon) model are solved numerically to simulate the flow through a cascade. The governing equations are solved for the entire flow domain, without the boundary layer assumptions. The stiffness of the k-epsilon equations is discussed. A semi-implicit, Runge-Kutta, time-marching scheme is developed to solve the k-epsilon equations. The impact of the k-epsilon solver on the explicit Runge-Kutta Navier-Stokes solver is discussed. Numerical solutions are presented for two dimensional turbulent flow over a flat plate and a double circular arc cascade and compared with experimental data.

Liu, Jong-Shang↗

NASA NTRS1988

Fast Euler solver for transonic airfoils. I - Theory. II - Applications

Equations written in terms of generalized Riemann variables are presently integrated by inverting six bidiagonal matrices and two tridiagonal matrices, using an implicit Euler solver that is based on the lambda-formulation. The solution is found on a C-grid whose boundaries are very close to the airfoil. The fast solver is then applied to the computation of several flowfields on a NACA 0012 airfoil at various Mach number and alpha values, yielding results that are primarily concerned with transonic flows. The effects of grid fineness and boundary distances are analyzed; the code is found to be robust and accurate, as well as fast.

Dadone, Andrea↗

NASA NTRS1988

3-D plume flow computations with an upwind solver

In the present study multi-nozzle plume flows are computed with a three-dimensional, Navier-Stokes solver. Numerical simulations are performed with the flux-split, two-factor, time symptotic, viscous flow solver. The two factor splitting provides a stable three-dimensional solution procedure under ideal-gas assumptions. Viscous, ideal-gas solutions for a thin lip symmetrical nozzle are compared with experimental and numerical solutions. Computed solutions to axisymmetric and three-dimensional, multi-nozzle problems at various altitudes and flight conditions demonstrate flow field complexity and three-dimensional effects.

Venkatapathy, Ethiraj↗

NASA NTRS1989

Transputer finite element solver

In January 1987, SPARTA received a Phase I SBIR award from the NASA Lewis Research Center to investigate the feasibility of a finite element solver implemented on multiple VLSI processors. The transputer was chosen as the processor for the feasibility study since it combined low cost with high performance and was specifically designed to directly link with other transputers to form networks of multiple processors. A brief description of transputers, a summary of the SBIR feasibility study, and a discussion of issues concerning a large scale transputer based finite element solver (TBFES) and the performance levels which can be expected are discussed.

Source record↗

NASA NTRS1988

The development of an intelligent interface to a computational fluid dynamics flow-solver code

Researchers at NASA Lewis are currently developing an 'intelligent' interface to aid in the development and use of large, computational fluid dynamics flow-solver codes for studying the internal fluid behavior of aerospace propulsion systems. This paper discusses the requirements, design, and implementation of an intelligent interface to Proteus, a general purpose, three-dimensional, Navier-Stokes flow solver. The interface is called PROTAIS to denote its introduction of artificial intelligence (AI) concepts to the Proteus code.

Williams, Anthony D.↗

NASA NTRS1989

Numerical solutions on a Pathfinder and other configurations using unstructured grids and a finite element solver

A three-dimensional unstructured grid generator and a finite element Euler solver are described. The grid generator uses the advancing front concept, and the flow solver is based on the flux corrected transport ideas. Several examples of computed flows past complete three-dimensional configurations are presented to demonstrate the flexibility and robustness of the programs. Current items requiring further attention are identified, and the progress over the last year toward them is reported.

Parikh, Paresh↗