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At least 217 records · Page 12

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DOE OSTI2025

A Simple, Scalable Large Deformation Solid Mechanics Implementation in the MOOSE Framework

This article describes a large deformation solid mechanics solver implemented as part of the freely available and open source MOOSE finite element simulation framework. The article documents the choices made in developing the solid mechanics framework and describes novel formulations for the gradient operator and constitutive modeling framework made to simplify implementations of different coordinate systems, stabilized gradient operators, and different constitutive model inputs and outputs. In the process, the article describes a new formulation that casts objective integration of the Cauchy stress as a linear transformation of the small stress rate. Finally, the article presents key implementation details and examines the parallel efficiency of the solid mechanics solver implemented in MOOSE. The implementation retains a good weak scaling efficiency beyond 1,000 parallel processes. The article includes a discussion of the factors limiting the parallel efficiency of implicit, large deformation solid mechanics codes on current high-performance computers, with the main current limitation being the scalability of the algebraic multigrid methods used to solve the linearized equilibrium equations.

Applied computing → Computer-aided design↗

DOE OSTI2024

Lifting MGARD: Construction of (pre)wavelets on the interval using polynomial predictors of arbitrary order

MGARD (MultiGrid Adaptive Reduction of Data) is an algorithm for compressing and refactoring scientific data, based on the theory of multigrid methods. The core algorithm is built around stable multilevel decompositions of conforming piecewise linear $C^0$ finite element spaces, enabling accurate error control in various norms and derived quantities of interest. In this work, we extend this construction to arbitrary order Lagrange finite elements $\mathbb{Q}_p$, $p \geq 0$, and propose a reformulation of the algorithm as a lifting scheme with polynomial predictors of arbitrary order. Additionally, a new formulation using a compactly supported wavelet basis is discussed, and an explicit construction of the proposed wavelet transform for uniform dyadic grids is described.

Reshniak, Viktor [Oak Ridge National Laboratory (O↗

NASA NTRS1981

Multigrid solution of the Navier-Stokes equations on nonuniform grids

The numerical solution of the Navier-Stokes equations in general two dimensional domains is considered. A proper finite difference approximation to the governing equations, on nonstaggered grids, in a transformed plane is formulated. Several aspects of a multigrid method for the solution of the finite difference equations are described. The efficiency of some relaxation schemes and the transfer among the grids which are nonuniform in the physical plane are emphasized.

Fuchs, L.↗

NASA NTRS1983

A preconditioned formulation of the Cauchy-Riemann equations

A preconditioning of the Cauchy-Riemann equations which results in a second-order system is described. This system is shown to have a unique solution if the boundary conditions are chosen carefully. This choice of boundary condition enables the solution of the first-order system to be retrieved. A numerical solution of the preconditioned equations is obtained by the multigrid method.

Phillips, T. N.↗

NASA NTRS1985

GRUMFOIL: A computer code for the viscous transonic flow over airfoils

A user's manual which describes the operation of the computer program, GRUMFOIL is presented. The program computes the viscous transonic flow over two dimensional airfoils using a boundary layer type viscid-inviscid interaction approach. The inviscid solution is obtained by a multigrid method for the full potential equation. The boundary layer solution is based on integral entrainment methods.

Mead, H. R.↗

NASA NTRS1986

Efficient solutions of two-dimensional incompressible steady viscous flows

A simple, efficient, and robust numerical technique is provided for solving two dimensional incompressible steady viscous flows at moderate to high Reynolds numbers. The proposed approach employs an incremental multigrid method and an extrapolation procedure based on minimum residual concepts to accelerate the convergence rate of a robust block-line-Gauss-Seidel solver for the vorticity-stream function Navier-Stokes equations. Results are presented for the driven cavity flow problem using uniform and nonuniform grids and for the flow past a backward facing step in a channel. For this second problem, mesh refinement and Richardson extrapolation are used to obtain useful benchmark solutions in the full range of Reynolds numbers at which steady laminar flow is established.

Morrison, J. H.↗

NASA NTRS1986

A multigrid LU-SSOR scheme for approximate Newton iteration applied to the Euler equations

A new efficient relaxation scheme in conjunction with a multigrid method is developed for the Euler equations. The LU SSOR scheme is based on a central difference scheme and does not need flux splitting for Newton iteration. Application to transonic flow shows that the new method surpasses the performance of the LU implicit scheme.

Yoon, Seokkwan↗

NASA NTRS1987

Vortex breakdown simulation based on a nonlinear inviscid model

It is shown that the inviscid equations governing steady axisymmetric flow with swirl, admit solutions with closed streamlines. Results are obtained using two different numerical algorithms. The first is based on a multigrid method for nonlinear eigenvalue problems, while the second is based on a least squares formulation.

Hafez, M. M.↗

NASA NTRS1988

Review of fatigue and fracture research at NASA Langley Research Center

Most dynamic components in helicopters are designed with a safe-life constant-amplitude testing approach that has not changed in many years. In contrast, the fatigue methodology in other industries has advanced significantly in the last two decades. Recent research at the NASA Langley Research Center and the U.S. Army Aerostructures Directorate at Langley are reviewed relative to fatigue and fracture design methodology for metallic components. Most of the Langley research was directed towards the damage tolerance design approach, but some work was done that is applicable to the safe-life approach. In the areas of testing, damage tolerance concepts are concentrating on the small-crack effect in crack growth and measurement of crack opening stresses. Tests were conducted to determine the effects of a machining scratch on the fatigue life of a high strength steel. In the area of analysis, work was concentrated on developing a crack closure model that will predict fatigue life under spectrum loading for several different metal alloys including a high strength steel that is often used in the dynamic components of helicopters. Work is also continuing in developing a three-dimensional, finite-element stress analysis for cracked and uncracked isotropic and anisotropic structures. A numerical technique for solving simultaneous equations called the multigrid method is being pursued to enhance the solution schemes in both the finite-element analysis and the boundary element analysis. Finally, a fracture mechanics project involving an elastic-plastic finite element analysis of J-resistance curve is also being pursued.

Everett, Richard A., Jr.↗

NASA NTRS1988

A diagonally inverted LU implicit multigrid scheme

A new Diagonally Inverted LU Implicit scheme is developed within the framework of the multigrid method for the 3-D unsteady Euler equations. The matrix systems that are to be inverted in the LU scheme are treated by local diagonalizing transformations that decouple them into systems of scalar equations. Unlike the Diagonalized ADI method, the time accuracy of the LU scheme is not reduced since the diagonalization procedure does not destroy time conservation. Even more importantly, this diagonalization significantly reduces the computational effort required to solve the LU approximation and therefore transforms it into a more efficient method of numerically solving the 3-D Euler equations.

Yokota, Jeffrey W.↗

NASA NTRS1988

Efficient solutions of two-dimensional incompressible steady viscous flows

Morrison, J. H.↗

NASA NTRS1988

A diagonally inverted LU implicit multigrid scheme

A new Diagonally Inverted LU Implicit scheme is developed within the framework of the multigrid method for the three-dimensional unsteady Euler equations. The matrix systems that are to be inverted in the LU scheme are treated by local diagonalizing transformations that decouple them into systems of scalar equations. Unlike the Diagonalized ADI method, the time accuracy of the LU scheme is not reduced since the diagonalizing procedure does not destroy time conservation. Even more importantly, this diagonalization significantly reduces the computational effort required to solve the LU approximation and therefore transforms it into a more efficient method of numerically solving the three-dimensional Euler equations.

Yokota, J. W.↗

NASA NTRS1988

A diagonally inverted LU implicit multigrid scheme for the 3-D Navier-Stokes equations and a two equation model of turbulence

An LU implicit multigrid algorithm is developed to calculate 3-D compressible viscous flows. This scheme solves the full 3-D Reynolds-Averaged Navier-Stokes equation with a two-equation kappa-epsilon model of turbulence. The flow equations are integrated by an efficient, diagonally inverted, LU implicit multigrid scheme while the kappa-epsilon equations are solved, uncoupled from the flow equations, by a block LU implicit algorithm. The flow equations are solved within the framework of the multigrid method using a four-grid level W-cycle, while the kappa-epsilon equations are iterated only on the finest grid. This treatment of the Reynolds-Averaged Navier-Stokes equations proves to be an efficient method for calculating 3-D compressible viscous flows.

Yokota, Jeffrey W.↗

NASA NTRS1989

A diagonally inverted LU implicit multigrid scheme for the 3-D Navier-Stokes equations and a two equation model of turbulence

Yokota, Jeffrey W.↗

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.↗

NASA NTRS1989

Hopf bifurcation in the driven cavity

Incompressible two dimensional calculations are reported for the impulsively started lid driven cavity with aspect ratio two. The algorithm is based on the time dependent streamfunction equation, with a Crank-Nicolson differencing scheme for the diffusion terms, and with an Adams-Bashforth scheme for the convection terms. A multigrid method is used to solve the linear implicit equations at each time step. Periodic asymptotic solutions have been found for Re = 10000 and for Re = 5000. The Re = 5000 results are validated by grid refinement calculations. The solutions are shown to be precisely periodic, and care is taken to demonstrate that asymptotic states were reached. A discussion is included about the indicators that are used to show that an asymptotic state was reached, and to show that the asymptotic state is indeed periodic.

Goodrich, John W.↗

NASA NTRS1990

On the parallel efficiency of the Frederickson-McBryan multigrid

To take full advantage of the parallelism in a standard multigrid algorithm requires as many processors as points. However, since coarse grids contain fewer points, most processors are idle during the coarse grid iterations. Frederickson and McBryan claim that retaining all points on all grid levels (using all processors) can lead to a superconvergent algorithm. The purpose of this work is to show that the parellel superconvergent multigrid (PSMG) algorithm of Frederickson and McBryan, though it achieves perfect processor utilization, is no more efficient than a parallel implementation of standard multigrid methods. PSMG is simply a new and perhaps simpler way of achieving the same results.

Decker, Naomi H.↗

NASA NTRS1990

Multigrid for hypersonic inviscid flows

The use of multigrid methods to solve the Euler equations for hypersonic flow is discussed. The steady state equations are considered with a Runge-Kutta smoother based on the time accurate equations together with local time stepping and residual smoothing. The effect of the Runge-Kutta coefficients on the convergence rate was examined considering both damping characteristics and convection properties. The importance of boundary conditions on the convergence rate for hypersonic flow is discussed. Also of importance are the switch between the second and fourth difference viscosity. Solutions are given for flow around the bump in a channel and flow around a biconic section.

Decker, Naomi H.↗