Unsteady Navier–Stokes solvers using hybrid spectral/hp element methods

Unsteady Navier - Stokes Solvers Using HybridSpectral /

A domain decomposition unsteady Stokes solver has been implemented in a hybrid spectral/hp element solver. To extend the algorithm to solve the Navier-Stokes equations the non-linear terms are explicitly advanced in time and treated as a forcing function to the Stokes solver. This scheme is compared with the computa-tionally eecient high order splitting method and it is found that for polynomia...

Parallel multi-level solvers for spectral element methods

Efficient solution of the Navier-Stokes equations in complex domains is dependent upon the availability of fast solvers for sparse linear systems. For unsteady incompressible flows, the pressure operator is the leading contributor to stiffness, as the characteristic propagation speed is infinite. In the context of operator splitting formulations, it is the pressure solve which is the most compu...

Hybrid Methods for Unsteady Fluid Flow Problems in Complex Geometries

New Hybrid Runge–Kutta Methods for Unsteady Reactive Flow Simulation

In the numerical simulation of transient reacting flow, standard explicit calculation is prohibitively expensive because of the small time steps needed to address the stiffness of a governing differential system. To circumvent this, new hybrid implicit–explicit methods proposed treat the stiffness, whereas the underlying time-step control is governed by the Courant stability criterion. Because ...

Variationally–based hybrid boundary element methods

The hybrid stress boundary element method (HSBEM) was introduced in 1987 on the basis of the Hellinger-Reissner potential, as a generalization of Pian’s hybrid finite element method. This new two-field formulation makes use of fundamental solutions to interpolate the stress field in the domain of an elastic body, which ends up discretized as a superelement with arbitrary shape and arbitrary num...