The linear analysis of turbomachinery aeroelasticity relies on the assumption of small level of unsteadiness and requires the solution of both the nonlinear steady and the linear unsteady flow equations. The objective of the analysis is to compute a complex flow solution that represents the amplitude and phase of the unsteady flow perturbation for the frequency of unsteadiness of interest. The ...

Numerical solutions to partial differential equations form the backbone of mathematical models that simulate the behavior of various electrochemical systems, specifically, batteries and fuel cells. In this paper, we present a set of numerical algorithms applied to efficiently solve this system of equations. These fast algorithms are identified by fully understanding the physics of the problem a...

In principle, the idea of parallel computing applied here and many other places is quite straightforward—divide and conquer. The overall parallel approach remains the same as before— domain decomposition, single program and multiple-data model, and message passing. The linear solver used here is the popular pre-conditioned GMRES approach. This method for reservoir simulation is totally reliant ...

In this paper, we report results of the performance, convergence, and accuracy of a parallel GMRES solver for Boundary Element Methods. The solver uses a hierarchical approximate matrix-vector product based on a hybrid Barnes-Hut / Fast Multipole Method. We study the impact of various accuracy parameters on the convergence and show that with minimal loss in accuracy, our solver yields significa...

The most popular iterative linear solvers in Computational Fluid Dynamics (CFD) calculations are restarted GMRES and BiCGStab. At the beginning of most incompressible flow calculations, the computation time and the number of iterations to converge for the pressure Poisson equation are quite high, since the initial guess is far from the solution. In this case, the BiCGStab algorithm, with relati...

A new Discrete Ordinates transport solver for unstructured tetrahedral meshes is presented. The uses the Discontinuous Galërkin Finite Element Method with linear or quadratic expansion of flux within each cell. solution one-group problem obtained non-preconditioned fixed-point GMRES iterations. Precision and performances are evaluated on 3D Radiation Transport Benchmark Problems proposed by Kob...

A Reynolds-averaged Navier-Stokes solver based on unstructured mesh techniques for analysis of high-lift configurations is described. The method makes use of an agglomeration multigrid solver for convergence acceleration. Implicit line-smoothing is employed to relieve the stiffness associated with highly stretched meshes. A GMRES technique is also implemented to speed convergence at the expense...

We propose an efficient solver for saddle point problems arising from finite element approximations of nonlocal multi-phase Allen--Cahn variational inequalities. The is seen to behave mesh independently and have only a very mild dependence on the number phase field variables. In addition we prove convergence, in three GMRES iterations, approximation two problem, regardless size or interfacial w...

Similarity solutions for the flow of granular materials are constructed. Unlike previous work, the present approach can be applied to non-axisymmetric containers. The steady state equations are reduced to a nonlinear Helmholtz on a subdomain of the sphere. Existence and local uniqueness of the solutions are established. A spectral numerical method using Fourier/ChebyshevGauss-Radau collocation ...