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Results for “implicit solvers”

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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At least 361 records · Page 20
All sourcesNASA NTRSDOE OSTI
NASA NTRS1981

Treatment of conical and nonconical supersonic flows by an implicit marching scheme applied to the full potential equation

An aerodynamic prediction technique based on the full potential equation in conservation form is developed for the treatment of supersonic flows. This technique bridges the gap between simplistic linear theory methods and complex Euler solvers. A novel local density linearization concept and a second order accurate retarded density scheme, both producing the correct artificial viscosity, are introduced in developing an implicit marching scheme for solving the scalar potential. Results for conical flows over delta wings and a wing-body combination and for non-conical flows over bodies of revolution at angles of attack are compared with Euler and nonconservative full potential calculations and experimental data. The present formulation requires an order of magnitude less computer time and significantly less computer memory over Euler codes and exhibits a considerable improvement in computational efficiency and generality over an existing nonconservative full potential code.

Shankar, V.↗
DOE OSTI2019

Adaptive Sparse Grid Discretization (ASGarD)

This code solves the Vlasov-Poisson equations in 6-dimensions without approximation. It uses sparse grid discretization to solve the high-dimensional PDEs. The code functions as a discontinuous Galerkin finite element solver. Advantages/benefits include no approximations, supports high-dimensionality, leadership-scale capability, and implicit time advance.

Hahn, Steven [Oak Ridge National Laboratory (ORNL)↗
NASA NTRS1985

Development of a boundary-layer-type solver based on simultaneous iteration technique for axisymmetric separated flows

A boundary-layer-type solver is developed for the numerical solution of axisymmetric separated flows. A new fully implicit coupling scheme for the viscous and inviscid regions is demonstrated. This fully implicit coupling technique is similar to the work of Carter, Veldman, and an extension of an earlier work of Halim and Hafez. A comparison is made for the convergence rate using this new fully implicit coupling technique and the semiimplicit coupling of Halim and Hafez. Numerical results using the fully implicit coupling are obtained for laminar incompressible separated flows, including a boattail and a series of trough geometries. Also, the near-wake flow problem is considered using the present formulation. A clear conclusion of this investigation is that the present scheme using the fully implicit coupling method converges at a faster rate than the semiimplicit coupling and the partially parabolized Navier-Stokes (PPNS) procedures.

Halim, A. A. M.↗
NASA NTRS1991

Development of a steady potential solver for use with linearized, unsteady aerodynamic analyses

A full potential steady flow solver (SFLOW) developed explicitly for use with an inviscid unsteady aerodynamic analysis (LINFLO) is described. The steady solver uses the nonconservative form of the nonlinear potential flow equations together with an implicit, least squares, finite difference approximation to solve for the steady flow field. The difference equations were developed on a composite mesh which consists of a C grid embedded in a rectilinear (H grid) cascade mesh. The composite mesh is capable of resolving blade to blade and far field phenomena on the H grid, while accurately resolving local phenomena on the C grid. The resulting system of algebraic equations is arranged in matrix form using a sparse matrix package and solved by Newton's method. Steady and unsteady results are presented for two cascade configurations: a high speed compressor and a turbine with high exit Mach number.

Hoyniak, Daniel↗
DOE OSTI2016

Application of Jacobian-free Newton–Krylov method in implicitly solving two-fluid six-equation two-phase flow problems: Implementation, validation and benchmark

This work represents a first-of-its-kind successful application to employ advanced numerical methods in solving realistic two-phase flow problems with two-fluid six-equation two-phase flow model. These advanced numerical methods include high-resolution spatial discretization scheme with staggered grids (high-order) fully implicit time integration schemes, and Jacobian-free Newton–Krylov (JFNK) method as the nonlinear solver. The computer code developed in this work has been extensively validated with existing experimental flow boiling data in vertical pipes and rod bundles, which cover wide ranges of experimental conditions, such as pressure, inlet mass flux, wall heat flux and exit void fraction. Additional code-to-code benchmark with the RELAP5-3D code further verifies the correct code implementation. The combined methods employed in this work exhibit strong robustness in solving two-phase flow problems even when phase appearance (boiling) and realistic discrete flow regimes are considered. Transitional flow regimes used in existing system analysis codes, normally introduced to overcome numerical difficulty, were completely removed in this work. As a result, this in turn provides the possibility to utilize more sophisticated flow regime maps in the future to further improve simulation accuracy.

42 ENGINEERING↗
DOE OSTI2015

A third-order implicit discontinuous Galerkin method based on a Hermite WENO reconstruction for time-accurate solution of the compressible Navier-Stokes equations

Here, a space and time third-order discontinuous Galerkin method based on a Hermite weighted essentially non-oscillatory reconstruction is presented for the unsteady compressible Euler and Navier–Stokes equations. At each time step, a lower-upper symmetric Gauss–Seidel preconditioned generalized minimal residual solver is used to solve the systems of linear equations arising from an explicit first stage, single diagonal coefficient, diagonally implicit Runge–Kutta time integration scheme. The performance of the developed method is assessed through a variety of unsteady flow problems. Numerical results indicate that this method is able to deliver the designed third-order accuracy of convergence in both space and time, while requiring remarkably less storage than the standard third-order discontinous Galerkin methods, and less computing time than the lower-order discontinous Galerkin methods to achieve the same level of temporal accuracy for computing unsteady flow problems.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1991

Computation of steady and unsteady compressible quasi-axisymmetric vortex flow and breakdown

The unsteady, compressible Navier-Stokes equations are used to compute and analyze compressible quasi-axisymmetric isolated vortices. The Navier-Stokes equations are solved using an implicit, upwind, flux-difference splitting finite-volume scheme. The developed three-dimensional solver has been verified by comparing its solution profiles with those of a slender, quasi-axisymmetric vortex solver for a subsonic, isolated quasi-axisymmetric vortex in an unbounded domain. The Navier-Stokes solver is then used to solve for a supersonic quasi-axisymmetric vortex flow in a configured circular duct. Steady and unsteady vortex-shock interactions and breakdown have been captured. The problem has also been calculated using the Euler solver of the same code and the results are compared with those of the Navier-Stokes solver. The effect of the initial swirl has been tentatively studied.

Kandil, Osama A.↗
NASA NTRS1992

Automatic differentiation of advanced CFD codes for multidisciplinary design

Automated multidisciplinary design of aircraft and other flight vehicles requires the optimization of complex performance objectives with respect to a number of design parameters and constraints. The effect of these independent design variables on the system performance criteria can be quantified in terms of sensitivity derivatives which must be calculated and propagated by the individual discipline simulation codes. Typical advanced CFD analysis codes do not provide such derivatives as part of a flow solution; these derivatives are very expensive to obtain by divided (finite) differences from perturbed solutions. It is shown that sensitivity derivatives can be obtained accurately and efficiently using the ADIFOR source translator for automatic differentiation. In particular, it is demonstrated that the 3-D, thin-layer Navier-Stokes, multigrid flow solver called TLNS3D is amenable to automatic differentiation in the forward mode even with its implicit iterative solution algorithm and complex turbulence modeling. It is significant that by using computational differentiation, consistent discrete nongeometric sensitivity derivatives have been obtained from an aerodynamic 3-D CFD code in a relatively short time, e.g., O(man-week) not O(man-year).

Bischof, C.↗
DOE OSTI2022

Time-discretization of a plasma-neutral MHD model with a semi-implicit leapfrog algorithm

The semi-implicit leapfrog time-discretization is a workhorse algorithm for initial-value MHD codes to bridge between vastly separated time scales. Inclusion of atomic interactions with neutrals breaks the functional structure of the MHD equations that exploited by the leapfrog. In this work, we address how to best integrate atomic physics into the semi-implicit leapfrog. Following the Crank-Nicolson method, one approach is to time-center the atomic interactions in the linear solver and use a Newton method to include the nonlinear contributions. Alternatively, another family of methods are based on operator-splitting the terms associated with the atomic interactions using a Strang-splitting technique. These methods naturally break equations into constituent ODE and PDE parts and preserve the structure exploited by the semi-implicit leapfrog. We study the accuracy and efficiency of these methods through a battery of 0D and 1D cases and show that a second-order-in-time Douglas-Rachford inspired coupling between the ODE and PDE advances is effective in reducing the time-discretization error to be comparable to that of Crank-Nicolson with Newton iteration of the nonlinear terms. Splitting ODE and PDE parts results in independent matrix solves for each field which reduces the computational cost considerably and provides parallelization over species relative to Crank-Nicolson.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2016

Varying stopping and self-focusing of intense proton beams as they heat solid density matter

Transport of intense proton beams in solid-density matter is numerically investigated using an implicit hybrid particle-in-cell code. Both collective effects and stopping for individual beam particles are included through the electromagnetic fields solver and stopping power calculations utilizing the varying local target conditions, allowing self-consistent transport studies. Two target heating mechanisms, the beam energy deposition and Ohmic heating driven by the return current, are compared. The dependences of proton beam transport in solid targets on the beam parameters are systematically analyzed, i.e., simulations with various beam intensities, pulse durations, kinetic energies, and energy distributions are compared. The proton beam deposition profile and ultimate target temperature show strong dependence on intensity and pulse duration. A strong magnetic field is generated from a proton beam with high density and tight beam radius, resulting in focusing of the beam and localized heating of the target up to hundreds of eV.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

Fast solvers for tokamak fluid models with PETSc

Multigrid (MG) is widely recognized as a highly effective solver for the model problem, the Laplacian, but textbook MG fails on most problems of interest. MG methods have been applied to complex, real-world applications with careful consideration of the physical model and discretization. In this work we develop the first step in applying MG methods to science and engineering relevant magnetohydrodynamics (MHD) tokamak models in the M3D-C1 (https://m3dc1.pppl.gov) fusion energy science code. The semi-implicit time integrator in M3D-C1 is composed of many linear solves. The implicit advance of the momentum equation is the most challenging and is the focus of this work. The current production solver in M3D-C1 is a block Jacobi (BJ) preconditioner within a Krylov solver, where blocks group degrees of freedom on planes of constant toroidal coordinate. BJ convergence degrades as the number of planes increases due to the spectral properties of the matrix preconditioned with BJ. The partially magnetic field-aligned, regular toroidal grid structure in M3D-C1 is amenable to semi-coarsening geometric MG in the toroidal direction. This paper develops such a solver and demonstrates competitive performance on a runaway electron model of a SPARC (https://cfs.energy/technology/sparc) disruption, and superior robustness on a stellarator model on which the BJ solver fails to converge.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Development of a Performance Portable Non-Equilibrium Plasma Fluid Solver on Adaptive Grids

This presentation will describe the numerical techniques, programming paradigms, verification, and performance of a non-equilibrium plasma fluid solver that can effectively utilize current and upcoming central processing and graphics processing unit (CPU+GPU) architectures. Our plasma fluid model solves the conservation equations for self-consistent electrostatic Poisson, electron and heavy species transport, and electron temperature on adaptive Cartesian grids. Our solver is written using performance portable adaptive mesh management library, AMReX (Zhang et al., JOSS, 4 (37) 1370, 2019), and can be built and run on widely available vendor specific GPU architectures (NVIDIA/AMD/Intel). We utilize a non-subcycled second order semi-implicit time-stepping method where all adaptive mesh refinement (AMR) levels are advanced with the same time step. The composite multi-level multigrid solver from within AMReX is used for each of the governing equations that are cast into a Helmholtz equation form. We have also developed a python based chemical mechanism parser framework that uses a similar format as CANTERA (Goodwin et al., Zenodo, 2018) yaml files as input. Our custom parser reads the yaml file and provides C++ files with transport and production rate functions that can be executed on both host (CPU) and device (GPU). We present verification of our solver using method of manufactured solutions that indicate formal second order accuracy with central diffusion and fifth order weighted-essentially-non-oscillatory (WENO) advection scheme. We also verify our solver with published literature on low-pressure capacitive and high-pressure streamer discharges. Our initial performance studies indicate 10X speed-up using 20 NVIDIA GPUs versus 200 CPUs for an atmospheric streamer discharge problem solved on a 512 x 1024 x 512 grid.

graphics processing units↗
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

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↗
DOE OSTI2021

An embedded variable step IMEX scheme for the incompressible Navier–Stokes equations

This report presents a series of implicit–explicit (IMEX) variable stepsize algorithms for the incompressible Navier–Stokes equations (NSE). Here, IMEX means the nonlinear term is treated fully explicitly while the remaining terms are treated implicitly. With the advent of new computer architectures there has been growing demand for low memory solvers of this type. The addition of time adaptivity improves the accuracy and greatly enhances the efficiency of the algorithm. We prove energy stability of an embedded first–second order IMEX pair. For the first order member of the pair, we prove stability for variable stepsizes, and analyze convergence. We believe this to be the first proof of this type for a variable stepsize IMEX scheme for the incompressible NSE. We then define and test a variable stepsize, variable order IMEX scheme using these methods. Our work contributes several firsts for IMEX NSE schemes, including an energy argument and error analysis of a two-step, variable stepsize method, and embedded error estimation for an IMEX multi-step method.

42 ENGINEERING↗
DOE OSTI2015

A high-order discontinuous Galerkin method with unstructured space–time meshes for two-dimensional compressible flows on domains with large deformations

We introduce a high-order accurate space-time discontinuous Galerkin method for solving two-dimensional compressible flow problems on fully unstructured space-time meshes. The discretization is based on a nodal formulation, with appropriate numerical fluxes for the first and the second-order terms, respectively. The scheme is implicit, and we solve the resulting non-linear systems using a parallel Newton-Krylov solver. The meshes are produced by a mesh moving technique with element connectivity updates, and the corresponding space-time elements are produced directly based on these local operations. To obtain globally conforming tetrahedral meshes, we first derive the required conditions on a prism boundary mesh to allow for a valid local triangulation. Next, we present an efficient algorithm for finding a global mesh that satisfies these conditions. We additionally show how to add and remove mesh nodes, again using local constructs for the space-time mesh. Our approach is demonstrated on a number of test problems, showing the high-order accuracy for model problems, and the ability to solve flow problems on domains with complex large deformations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

A scalable, fully implicit algorithm for the reduced two-field low-β extended MHD model

Here, we demonstrate a scalable fully implicit algorithm for the two-field low-β extended MHD model. This reduced model describes plasma behavior in the presence of strong guide fields, and is of significant practical impact both in nature and in laboratory plasmas. The model displays strong hyperbolic behavior, as manifested by the presence of fast dispersive waves, which make a fully implicit treatment very challenging. In this study, we employ a Jacobian-free Newton–Krylov nonlinear solver, for which we propose a physics-based preconditioner that renders the linearized set of equations suitable for inversion with multigrid methods. As a result, the algorithm is shown to scale both algorithmically (i.e., the iteration count is insensitive to grid refinement and timestep size) and in parallel in a weak-scaling sense, with the wall-clock time scaling weakly with the number of cores for up to 4096 cores. For a 4096 × 4096 mesh, we demonstrate a wall-clock-time speedup of ~6700 with respect to explicit algorithms. The model is validated linearly (against linear theory predictions) and nonlinearly (against fully kinetic simulations), demonstrating excellent agreement.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗