β Scribed by Armfield, S. W. ;Fletcher, C. A. J.
No coin nor oath required. For personal study only.
Order-of-magnitude deletion of the stream-wise diffusion terms leads to a reduced form of the Navier-Stokes equations. Solving the reduced equations for internal flows with single-sweep marching algorithms requires a severe minimum stream-wise step-size to avoid unstable solutions. This behaviour is shown to be predominantly due to a single term in the cross-stream momentum equation, uv.,, which introduces a strong elliptic character into the equations. An order-of-magnitude deletion of this term reduces the minimum stream-wise step-size sufficiently for accurate solutions to be obtained. Further reduction of the transverse momentum equation on an order-of-magnitude basis removes all cross-stream velocity derivatives and completely eliminates the minimum stream-wise step-size condition for both swirling and non-swirling flows.
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π SIMILAR VOLUMES
The stability of a finite difference discretization of the time-dependent incompressible Navier-Stokes equations in velocity-pressure formulation is studied. In paticular, we compare the stability for different pressure boundary conditions in a semiimplicit time-integration scheme. where only the vi
The compressible Navier-Stokes equations for viscous ows with general large continuous initial data, as well as with large discontinuous initial data, are studied. Both a homogeneous free boundary problem with zero outer pressure and a ΓΏxed boundary problem are considered. For the large initial data
Finite element solutions of the Euler and Navier-Stokes equations are presented, using a simple dissipation model. The discretization is based on the weak-Galerkin weighted residual method and equal interpolation functions for all the unknowns are permitted. The nonlinearity is iterated upon using a