New classes of optimal splittingup schemes for the computation of transient flows
Abstract
Classes of explicit secondorder splittingup disintegration schemes are first presented for solving the threedimensional Euler equations, and full timedependent compressible viscous NavierStokes equations of fluid mechanics. Some results, obtained for transient threedimensional flows, are given. They show that these schemes are welladapted to compute such flows. New classes of 'optimal' second order schemes are then examined: an explicit 'dissipationoptimal' class (defined as dissipative with minimal dissipation), and 'timeoptimal' classes (in the sense that they allow optimal time steps). The first class yields a shock profile without oscillations for an unsteady shock problem. The second classes use explicit, implicit or hybrid (implicit or explicit), and and hybrid disintegrationhopscotch schemes. The 'timeoptimal' explicit method should be quicker than the other existing explicit splittingup methods, and as efficient as implicit methods for solving inviscid or viscous transient flows.
 Publication:

ONERA
 Pub Date:
 1984
 Bibcode:
 1984nmtc.conf.....L
 Keywords:

 Computational Fluid Dynamics;
 Finite Difference Theory;
 Oscillating Flow;
 Three Dimensional Flow;
 Euler Equations Of Motion;
 Inviscid Flow;
 NavierStokes Equation;
 Shock Wave Propagation;
 Transient Response;
 Fluid Mechanics and Heat Transfer