Long-Wavelength Instability in Surface-Tension-Driven Benard Convection

Laboratory studies reveal a deformational instability that leads to a drained region (dry spot) in an initially flat liquid layer (with a free upper surface) heated uniformly from below. This long-wavelength instability supplants hexagonal convection cells as the primary instability in viscous liquid layers that are sufficiently thin or are in microgravity. The instability occurs at a temperature gradient 34% smaller than predicted by linear stability theory. Numerical simulations show a drained region qualitatively similar to that seen in the experiment.Comment: 4 pages. The RevTeX file has a macro allowing various styles. The appropriate style is "mypprint" which is the defaul

The CSP Method for Simplifying Kinetics

The Computational Singular Perturbation (CSP) method of simplified kinetics modeling is presented with emphasis on its comparative merits versus conventional methodologies. A new "refinement" procedure for the basis vectors spanning the fast reaction subspace is presented. A simple example is first worked through using the conventional partial-equilibrium and quasi-steady approximations, and is then treated in some detail using CSP

Explicit Time-Scale Splitting Algorithm For Stiff Problems: Auto-Ignition Of Gaseous-Mixtures Behind A Steady Shock

A new explicit algorithm based on the computational singular perturbation (CSP) method is presented. This algorithm is specifically designed to solve stiff problems, and its performance increases with stiffness. The key concept in its structure is the splitting of the fast from the slow time scales in the problem, realized by embedding CSP concepts into an explicit scheme. In simple terms, the algorithm marches in time with only the terms producing the slow time scales, while the contribution of the terms producing the fast time scales is taken into account at the end of each integration step as a correction. The new algorithm is designed for the integration of stiff systems of PDEs by means of explicit schemes. For simplicity in the presentation and discussion of the different features of the new algorithm, a simple test case is considered, involving the auto-ignition of a methane/air mixture behind a normal shock wave, which is described by a system of ODEs. The performance of the new algorithm (accuracy and computational efficiency) is then compared with the well- known LSODE package. Its merits when used for the solution of systems of PDEs are discussed. Although when dealing with a stiff system of ODEs the new algorithm is shown to provide equal accuracy with that delivered by LSODE at the cost of higher execution time, the results indicate that its performance could be superior when facing a stiff system of PDEs

An Explicit Time-Scale Splitting Algorithm for Stiff ODE’s

Heidelberg, Germani

The origin of CEMA and its relation to CSP

There currently exist two methods for analysing an explosive mode introduced by chemical kinetics in a reacting process: the Computational Singular Perturbation (CSP) algorithm and the Chemical Explosive Mode Analysis (CEMA). CSP was introduced in 1989 and addressed both dissipative and explosive modes encountered in the multi-scale dynamics that characterize the process, while CEMA was introduced in 2009 and addressed only the explosive modes. It is shown that (i) the algorithmic tools incorporated in CEMA were developed previously on the basis of CSP and (ii) the examination of explosive modes has been the subject of CSP-based works, reported before the introduction of CEMA

Adaptive simplification of complex multiscale systems

A fully adaptive methodology is developed for reducing the complexity of large dissipative systems. This represents a significant step toward extracting essential physical knowledge from complex systems, by addressing the challenging problem of a minimal number of variables needed to exactly capture the system dynamics. Accurate reduced description is achieved, by construction of a hierarchy of slow invariant manifolds, with an embarrassingly simple implementation in any dimension. The method is validated with the autoignition of the hydrogen-air mixture where a reduction to a cascade of slow invariant manifolds is observe