{"id":3939,"date":"2016-05-19T23:15:46","date_gmt":"2016-05-20T03:15:46","guid":{"rendered":"http:\/\/mseas.mit.edu\/?p=3939"},"modified":"2022-11-21T21:29:47","modified_gmt":"2022-11-22T02:29:47","slug":"an-iterative-pressure-correction-method-for-the-unsteady-incompressible-navier-stokes-equation","status":"publish","type":"post","link":"https:\/\/mseas.mit.edu\/?p=3939","title":{"rendered":"An Iterative Pressure-Correction Method for the Unsteady Incompressible Navier-Stokes Equation"},"content":{"rendered":"The pressure-correction projection method for the incompressible Navier-Stokes equation\nis approached as a preconditioned Richardson iterative method for the pressure-\nSchur complement equation. Typical pressure correction methods perform only one\niteration and suffer from a splitting error that results in a spurious numerical boundary\nlayer, and a limited order of convergence in time. We investigate the benefit of\nperforming more than one iteration.\nWe show that that not only performing more iterations attenuates the effects\nof the splitting error, but also that it can be more computationally efficient than\nreducing the time step, for the same level of accuracy. We also devise a stopping\ncriterion that helps achieve a desired order of temporal convergence, and implement\nour method with multi-stage and multi-step time integration schemes. In order to\nfurther reduce the computational cost of our iterative method, we combine it with an\nAitken acceleration scheme.\nOur theoretical results are validated and illustrated by numerical test cases for\nthe Stokes and Navier-Stokes equations, using Implicit-Explicit Backwards Difference\nFormula and Runge-Kutta time integration solvers. The test cases comprises a now\nclassical manufactured solution in the projection method literature and a modified\nversion of a more recently proposed manufactured solution.","protected":false},"excerpt":{"rendered":"<p>The pressure-correction projection method for the incompressible Navier-Stokes equation is approached as a preconditioned Richardson iterative method for the pressure- Schur complement equation. Typical pressure correction methods perform only one iteration and suffer from a splitting error that results in a spurious numerical boundary layer, and a limited order of convergence in time. We investigate [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[42,5,44],"tags":[],"class_list":["post-3939","post","type-post","status-publish","format-standard","hentry","category-meche-theses","category-publications","category-masters-theses"],"_links":{"self":[{"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=\/wp\/v2\/posts\/3939","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=3939"}],"version-history":[{"count":1,"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=\/wp\/v2\/posts\/3939\/revisions"}],"predecessor-version":[{"id":3940,"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=\/wp\/v2\/posts\/3939\/revisions\/3940"}],"wp:attachment":[{"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=3939"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=3939"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=3939"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}