Mathematically, the pressure has no boundary conditions, but in the fractional step method, dp/dn=0 is applied to solve the pressure Poisson equation \nabla^2 p=1/dt div u* (here u* is an intermediate velocity). Hence, my question is: do the results by the fractional step method be equivalent to that by the original NS equations?
The boundary condition used for the pressure, as you wrote, is not a physical condition. It was introduced, following Chorin, "Numerical Solution of the Navier-Stokes Equations" (1968), as a condition that could reproduce the previous simulations done with the artificial compressibility method. Numerical tests show that such an additional condition gives very robust results in good agreement with experiments and it is largely employed. For high-order methods, a correction of this condition is adopted.
Mathematically, the pressure has no boundary conditions, but in the fractional step method, dp/dn=0 is applied to solve the pressure Poisson equation \nabla^2 p=1/dt div u* (here u* is an intermediate velocity). Hence, my question is: do the results by the fractional step method be equivalent to that by the original NS equations?
ReplyDeleteThe boundary condition used for the pressure, as you wrote, is not a physical condition. It was introduced, following Chorin, "Numerical Solution of the Navier-Stokes Equations" (1968), as a condition that could reproduce the previous simulations done with the artificial compressibility method. Numerical tests show that such an additional condition gives very robust results in good agreement with experiments and it is largely employed. For high-order methods, a correction of this condition is adopted.
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