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Projection Step (projection + step)

Distribution by Scientific Domains

Engineering	75%

Selected Abstracts

A collocated, iterative fractional-step method for incompressible large eddy simulation

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2008
Giridhar Jothiprasad
Abstract Fractional-step methods are commonly used for the time-accurate solution of incompressible Navier,Stokes (NS) equations. In this paper, a popular fractional-step method that uses pressure corrections in the projection step and its iterative variants are investigated using block-matrix analysis and an improved algorithm with reduced computational cost is developed. Since the governing equations for large eddy simulation (LES) using linear eddy-viscosity-based sub-grid models are similar in form to the incompressible NS equations, the improved algorithm is implemented in a parallel LES solver. A collocated grid layout is preferred for ease of extension to curvilinear grids. The analyzed fractional-step methods are viewed as an iterative approximation to a temporally second-order discretization. At each iteration, a linear system that has an easier block-LU decomposition compared with the original system is inverted. In order to improve the numerical efficiency and parallel performance, modified ADI sub-iterations are used in the velocity step of each iteration. Block-matrix analysis is first used to determine the number of iterations required to reduce the iterative error to the discretization error of. Next, the computational cost is reduced through the use of a reduced stencil for the pressure Poisson equation (PPE). Energy-conserving, spatially fourth-order discretizations result in a 7-point stencil in each direction for the PPE. A smaller 5-point stencil is achieved by using a second-order spatial discretization for the pressure gradient operator correcting the volume fluxes. This is shown not to reduce the spatial accuracy of the scheme, and a fourth-order continuity equation is still satisfied to machine precision. The above results are verified in three flow problems including LES of a temporal mixing layer. Copyright © 2008 John Wiley & Sons, Ltd. [source]

Implementing a proximal algorithm for some nonlinear multicommodity flow problems

NETWORKS: AN INTERNATIONAL JOURNAL, Issue 1 2007
Adam Ouorou
Abstract In this article, we consider applying a proximal algorithm introduced by Ouorou to some convex multicommodity network flow minimization problems. This algorithm follows the characterization of saddle points introduced earlier but can be derived from Martinet's proximal algorithm. In the primal space, the algorithm can be viewed as a regularized version of the projection algorithm by Rosen. A remarkable feature of the algorithm is that the projection step for multicommodity flow problems reduces to solving independent linear systems (one for each commodity) involving the node-arc incidence matrix of the network. The algorithm is therefore amenable to parallel implementation. We present some numerical results on large-scale routing problems arising in telecommunications and quadratic multicommodity flow problems. A comparison with a specialized code for multicommodity flow problems indicates that this proximal algorithm is specially designed for very large-scale instances. © 2006 Wiley Periodicals, Inc. NETWORKS, Vol. 49(1), 18,27 2007 [source]

Natural gradient-projection algorithm for distribution control

OPTIMAL CONTROL APPLICATIONS AND METHODS, Issue 5 2009
Zhenning Zhang
Abstract In this paper, we use an information geometric algorithm to solve the distribution control problem. Here, we consider the distribution of the output determined by the control input only. We set up two manifolds that are formed by the B-spline functions and the system output probability density functions, and we call them the B-spline manifold(B) and the system output manifold(M), respectively. Moreover, we call the new designed algorithm natural gradient-projection algorithm. In the natural gradient step, we use natural gradient algorithm to obtain an optimal trajectory of the weight vector on the B-spline manifold from the viewpoint of information geometry. In the projection step, we project the selected points on B onto M. The coordinates of the projections on M give the trajectory of the control input u. Copyright © 2008 John Wiley & Sons, Ltd. [source]

Accelerating iterative solution methods using reduced-order models as solution predictors

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 5 2006
R. Markovinovi
Abstract We propose the use of reduced-order models to accelerate the solution of systems of equations using iterative solvers in time stepping schemes for large-scale numerical simulation. The acceleration is achieved by determining an improved initial guess for the iterative process based on information in the solution vectors from previous time steps. The algorithm basically consists of two projection steps: (1) projecting the governing equations onto a subspace spanned by a low number of global empirical basis functions extracted from previous time step solutions, and (2) solving the governing equations in this reduced space and projecting the solution back on the original, high dimensional one. We applied the algorithm to numerical models for simulation of two-phase flow through heterogeneous porous media. In particular we considered implicit-pressure explicit-saturation (IMPES) schemes and investigated the scope to accelerate the iterative solution of the pressure equation, which is by far the most time-consuming part of any IMPES scheme. We achieved a substantial reduction in the number of iterations and an associated acceleration of the solution. Our largest test problem involved 93 500 variables, in which case we obtained a maximum reduction in computing time of 67%. The method is particularly attractive for problems with time-varying parameters or source terms. Copyright © 2006 John Wiley & Sons, Ltd. [source]