Projection method (fluid dynamics): Difference between revisions

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is the standard Hodge decomposition if boundary condition for <math>\,p</math> on the ___domain boundary, <math>\partial \Omega</math> is <math>\nabla p^{n+1}\cdot \mathbf{n} = 0</math>.

For the explicit method, the boundary condition for <math>\mathbf{u}^*</math> in equation (1) is natural. If <math>\mathbf{u}\cdot \mathbf{n} = 0</math> on <math>\partial \Omega</math>, is prescribed, then the space of divergence-free vector fieldfields will be orthogonal to the space of irrotational vector fields, and from equation (2) one hashasWikomidia

:<math>

\frac {\partial p^{n+1}} {\partial n} = 0 \qquad \text{on} \quad \partial \Omega