Projection method (fluid dynamics): Difference between revisions

Revision as of 08:34, 16 January 2015

Revision as of 22:50, 16 January 2015

Line 4:

| surname1 = Chorin

| given1 = A. J.

| title = AThe numerical methodsolution forof solvingthe incompressibleNavier-Stokes viscousequations flowfor an incompressible problemsfluid

| journal = JournalBull. ofAm. ComputationalMath. Soc. Physics

| volume = 2273

| year = 1967

| pages = 12928–26931

| url =http://math.berkeley.edu/~chorin/chorin67.pdf

,}}</ref>

}}</ref> as an efficient means of solving the incompressible [[Navier-Stokes equation]]s. The key advantage of the projection method is that the computations of the velocity and the pressure fields are decoupled.

<ref>

{{Citation

| surname1 = Chorin

| given1 = A. J.

| title = Numerical Solution of the Navier-Stokes Equations

| journal = Math. Comp.

| volume = 22

| year = 1968

| pages = 745&ndash;762

| url =

| doi=10.1090/s0025-5718-1968-0242392-2

}}</ref>

}}</ref> as an efficient means of solving the incompressible [[Navier-Stokes equation]]s. The key advantage of the projection method is that the computations of the velocity and the pressure fields are decoupled.

==The algorithm==

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</math>

In [[Alexandre Chorin|Chorin]]'s original version of the projection method, one first computes an intermediate velocity, <math>\mathbf{u}^*</math>, explicitly using the momentum equation by ignoring the pressure gradient term:

,<ref>

{{Citation

| surname1 = Chorin

| given1 = A. J.

| title = Numerical Solution of the Navier-Stokes Equations

| journal = Math. Comp.

| volume = 22

| year = 1968

| pages = 745&ndash;762

| url =

| doi=10.1090/s0025-5718-1968-0242392-2

}}</ref> one first computes an intermediate velocity, <math>\mathbf{u}^*</math>, explicitly using the momentum equation by ignoring the pressure gradient term:

:<math>