Projection method (fluid dynamics): Difference between revisions

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The '''projection method''' is an effective means of [[Numerical analysis|numerically]] solving time-dependent [[incompressible flow|incompressible fluid-flow]] problems. It was originally introduced by [[Alexandre Chorin]] in 1967 and independently by [[Roger Temam]]<ref>

{{Citation

{{Harvard reference

| Surname1surname1 = Temam

| Given1given1 = R.

| Titletitle = Une m&eacute;thode d'approximation des solutions des &eacute;quations Navier-Stokes,

| Journaljournal = Bull. Soc. Math. France

| Volumevolume = 98

| Yearyear = 1968

| Pagespages = 115&ndash;152

| url =

}}</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.

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In Chorin's original version of the projection method

<ref>

{{Citation

{{Harvard reference

| Surname1surname1 = Chorin

| Given1given1 = A. J.

| Titletitle = Numerical Solution of the Navier-Stokes Equations

| Journaljournal = Math. Comp.

| Volumevolume = 22

| Yearyear = 1968

| Pagespages = 745&ndash;762

| url =

}}</ref>, the intermediate velocity, <math>\mathbf{u}^*</math>, is explicitly computed using the momentum equation ignoring the pressure gradient term: