A symmetry-preserving discretisation and regularisation model for compressible flow with application to turbulent channel flow

Most simulation methods for compressible flow attain numerical stability at the cost of swamping the fine turbulent flow structures by artificial dissipation. This article demonstrates that numerical stability can also be attained by preserving conservation laws at the discrete level. A new mathematical explanation of conservation in compressible flow reveals that many conservation properties of convection are due to the skew-symmetry of the convection operator. By preserving this skew-symmetry at the discrete level, a fourth-order accurate collocated symmetry-preserving discretisation with excellent conservation properties is obtained. Also a new symmetry-preserving regularisation subgrid-scale model is proposed. The proposed techniques are assessed in simulations of compressible turbulent channel flow. The symmetry-preserving discretisation for compressible flow has good stability without artificial dissipation and yields acceptable results already on coarse grids. Regularisation does not consistently improve upon no-model results, but often compares favourably with eddy-viscosity models.     

A model for the enzyme activity in systems with large composition fluctuations. An application to the unusual kinetics of phospholipase A2

A non-equilibrium thermodynamics based model is proposed in order to describe the role of large concentration fluctuations of enzymes, reactants and products in modulating the macroscopic time evolution of chemical kinetics. The encounter probabilities between reactants and enzyme depend on their local concentration. Fluctuations modify the bimolecular encounter probability. Since, in turn, the amplitude of fluctuations depends itself on the instantaneous composition of the reacting mixture, the time-varying chemical composition acts as a positive feedback mechanism for the reactive fluid mixture near the critical temperature for phase separation. The model is applied to rationalize the unusual features of phospholipase kinetics, an enzyme which catalyzes the hydrolisis of membrane forming phospholipids, yielding products which are still soluble in the lipid matrix. A typical feature of the enzyme reaction is the long induction time prior to a ”burst” of activity. This effect is well reproduced by the theory, together with the dependence of the induction time on the exogeneous addition of products or other liposoluble substances, the effects of enzyme and substrate concentration, and the temperature dependence of the enzyme activation. All these properties emerge as a consequence of the coupling between enconter probability and time-varying bilayer heterogeneity. A good qualitative agreement between theoretical results and the available experimental results has been generally found. Received: 25 June 1996 / Revised: 17 April 1997 / Accepted: 26 November 1997