%0 Journal Article %1 saleri2005pressure %A Saleri, F. %A Veneziani, A. %D 2005 %I Society for Industrial & Applied Mathematics (SIAM) %J SIAM Journal on Numerical Analysis %K 35q30-navier-stokes-equations 65m12-pdes-ivps-stability-and-convergence-of-numerical-methods 76d05-incompressible-navier-stokes-equations %N 1 %P 174--194 %R 10.1137/s0036142903435429 %T Pressure Correction Algebraic Splitting Methods for the Incompressible Navier--Stokes Equations %U https://epubs.siam.org/doi/10.1137/S0036142903435429 %V 43 %X In this paper we present a new family of methods for the effective numerical solution of the incompressible unsteady Navier--Stokes equations. These methods resort to an algebraic splitting of the discretized problem based on inexact LU block factorizations of the corresponding matrix (following A. Quarteroni, F. Saleri, and A. Veneziani, Comput. Methods Appl. Mech. Engrg., 188 (2000), pp. 505--526. In particular, we will start from inexact algebraic factorizations of algebraic Chorin--Temam and Yosida type and introduce a pressure correction step aimed at improving the time accuracy. One of the schemes obtained in this way (the algebraic Chorin--Temam pressure correction method) resembles a method previously introduced in the framework of differential projection schemes (see L. Timmermans, P. Minev, and F. V. de Vosse, Internat. J. Numer. Methods Fluids, 22 (1996), pp. 673--688, A. Prohl, Projection and Quasi-Compressibility Methods for Solving the Incompressible Navier--Stokes Equations, Teubner, Stuttgart, 1997. The stability and the dependence of splitting error on the time step of the new methods is investigated and tested on several numerical cases.

@article{saleri2005pressure, abstract = { In this paper we present a new family of methods for the effective numerical solution of the incompressible unsteady Navier--Stokes equations. These methods resort to an algebraic splitting of the discretized problem based on inexact LU block factorizations of the corresponding matrix (following [A. Quarteroni, F. Saleri, and A. Veneziani, Comput. Methods Appl. Mech. Engrg., 188 (2000), pp. 505--526]. In particular, we will start from inexact algebraic factorizations of algebraic Chorin--Temam and Yosida type and introduce a pressure correction step aimed at improving the time accuracy. One of the schemes obtained in this way (the algebraic Chorin--Temam pressure correction method) resembles a method previously introduced in the framework of differential projection schemes (see [L. Timmermans, P. Minev, and F. V. de Vosse, Internat. J. Numer. Methods Fluids, 22 (1996), pp. 673--688], [A. Prohl, Projection and Quasi-Compressibility Methods for Solving the Incompressible Navier--Stokes Equations, Teubner, Stuttgart, 1997]. The stability and the dependence of splitting error on the time step of the new methods is investigated and tested on several numerical cases.}, added-at = {2020-06-18T03:43:51.000+0200}, author = {Saleri, F. and Veneziani, A.}, biburl = {https://www.bibsonomy.org/bibtex/21b712499617a256496e05e9e20aaa74a/gdmcbain}, doi = {10.1137/s0036142903435429}, interhash = {dd8a8c2aae1945b5069732fc8adca430}, intrahash = {1b712499617a256496e05e9e20aaa74a}, journal = {{SIAM} Journal on Numerical Analysis}, keywords = {35q30-navier-stokes-equations 65m12-pdes-ivps-stability-and-convergence-of-numerical-methods 76d05-incompressible-navier-stokes-equations}, month = jan, number = 1, pages = {174--194}, publisher = {Society for Industrial {\&} Applied Mathematics ({SIAM})}, timestamp = {2020-06-18T03:43:51.000+0200}, title = {Pressure Correction Algebraic Splitting Methods for the Incompressible Navier--Stokes Equations}, url = {https://epubs.siam.org/doi/10.1137/S0036142903435429}, volume = 43, year = 2005 }