Number Of Sub-iterations Research Articles

A domain decomposition approach to accelerate simulations of structure preserving nematic liquid crystal models

We present a method for speeding up equilibrium simulations of liquid crystals for two related models that are degenerate with respect to defects: the Ericksen model and the uniaxially constrained Landau-de Gennes model. The degeneracy induces a non-linear/non-smooth coupling between the two order parameters in both models that makes the discrete problems very stiff to solve. The technique described in this paper uses an alternating Schwarz domain decomposition method that isolates the degenerate region and alleviates some of the stiffness, and is easy to implement. We present numerical results illustrating the speed-up and how it is affected by the size of the sub-domains and the number of sub-iterations used within the degenerate region.

Computational Fluid Dynamics Algorithms for Unsteady Shock-Induced Combustion, Part 2: Comparison

Acomputational study is carried out to develop a fully implicit and time-accuratecomputational e uid dynamics code for the analysis of reactive e ow systems. Periodically oscillating shock-induced combustion around a blunt body in a stoichiometric hydrogen ‐air mixture is used as a validation problem of examining various numerical considerations. Euler equations and species conservation equations are used as the governing equations for the chemically reacting e ow. Spatial discretization of the governing equation is based on Roe’ s approximate Riemann solver with a MUSCL-type total variation diminishing scheme for higher-order spatial resolution. The secondorder-accuratetimeintegrationmethodisbasedonalower ‐uppersymmetricGauss ‐Seidelscheme,usingaNewton subiteration method and Steger ‐Warming e ux Jacobian splitting. As a e rst step of the validation procedure, simulations of experimental results were carried out to cone rm the reliability of the baseline method. In the next step, the general aspects of the baseline method were examined, including order of time integration, number of subiterations, and use of approximate e ux Jacobian splitting. Appropriateness of the grid system is also examined by using a grid ree nement study.