%0 Journal Article %1 citeulike:6615630 %A Klaij, C. %A van der Vegt, J. %A van der Ven, H. %D 2006 %J Journal of Computational Physics %K 76m10-finite-element-methods-in-fluid-mechanics 65n30-pdes-bvps-finite-elements %N 2 %P 622--643 %R 10.1016/j.jcp.2006.04.003 %T Pseudo-time Stepping Methods for Space–Time Discontinuous Galerkin Discretizations of the Compressible Navier–Stokes Equations %U http://dx.doi.org/10.1016/j.jcp.2006.04.003 %V 219 %X The space–time discontinuous Galerkin discretization of the compressible Navier–Stokes equations results in a non-linear system of algebraic equations, which we solve with pseudo-time stepping methods. We show that explicit Runge–Kutta methods developed for the Euler equations suffer from a severe stability constraint linked to the viscous part of the equations and propose an alternative to relieve this constraint while preserving locality. To evaluate its effectiveness, we compare with an implicit–explicit Runge–Kutta method which does not suffer from the viscous stability constraint. We analyze the stability of the methods and illustrate their performance by computing the flow around a 2D airfoil and a 3D delta wing at low and moderate Reynolds numbers.

@article{citeulike:6615630, abstract = {{The space–time discontinuous Galerkin discretization of the compressible Navier–Stokes equations results in a non-linear system of algebraic equations, which we solve with pseudo-time stepping methods. We show that explicit Runge–Kutta methods developed for the Euler equations suffer from a severe stability constraint linked to the viscous part of the equations and propose an alternative to relieve this constraint while preserving locality. To evaluate its effectiveness, we compare with an implicit–explicit Runge–Kutta method which does not suffer from the viscous stability constraint. We analyze the stability of the methods and illustrate their performance by computing the flow around a 2D airfoil and a 3D delta wing at low and moderate Reynolds numbers.}}, added-at = {2017-06-29T07:13:07.000+0200}, author = {Klaij, C. and van der Vegt, J. and van der Ven, H.}, biburl = {https://www.bibsonomy.org/bibtex/2c0bdc36b525934b0029130a9f3ee9e1a/gdmcbain}, citeulike-article-id = {6615630}, citeulike-attachment-1 = {klaij_06_pseudotime_33727.pdf; /pdf/user/gdmcbain/article/6615630/33727/klaij_06_pseudotime_33727.pdf; 55b3cbcfc817154be29d1be2caeac90d853ca36d}, citeulike-linkout-0 = {http://dx.doi.org/10.1016/j.jcp.2006.04.003}, comment = {(private-note)I found this searching the 'net for "von Neumann number"; it defines it in (5) (on p. 10 of the attached preprint) as \$d \Delta t/(\Delta x)^2\$, where d is the diffusivity.}, day = 10, doi = {10.1016/j.jcp.2006.04.003}, file = {klaij_06_pseudotime_33727.pdf}, interhash = {2b67b4a46fa1f340f4b53e34c101dc6c}, intrahash = {c0bdc36b525934b0029130a9f3ee9e1a}, issn = {00219991}, journal = {Journal of Computational Physics}, keywords = {76m10-finite-element-methods-in-fluid-mechanics 65n30-pdes-bvps-finite-elements}, month = dec, number = 2, pages = {622--643}, posted-at = {2010-02-03 02:30:47}, priority = {2}, timestamp = {2019-02-28T23:44:01.000+0100}, title = {Pseudo-time Stepping Methods for Space–Time Discontinuous {G}alerkin Discretizations of the Compressible {N}avier–{S}tokes Equations}, url = {http://dx.doi.org/10.1016/j.jcp.2006.04.003}, volume = 219, year = 2006 }