Implicit Solutions of the Unsteady Navier-Stokes Equation for Laminar Flow Through an Orifice,
NAVAL SHIP RESEARCH AND DEVELOPMENT CENTER BETHESDA MD
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The Navier-Stokes and the continuity equations are rearranged into a vorticity transport equation and a definition of vorticity equation. One thus obtains two elliptical partial differential equations in the two variables of vorticity and stream function. Implicit finite difference forms of the equations are developed which are fourth-order accurate in space and second-order accurate in time. Grid networks were imposed on the flow field. Initial conditions were designated to be either 1 no flow in the case of the first time step or 2 the results from the previous time step. Solutions were obtained from one time step to the next by iterating the vorticity transport and definition of vorticity equations together with the appropriate boundary conditions.
- Numerical Mathematics
- Fluid Mechanics