TY - JOUR

T1 - Isogeometric residual minimization (iGRM) for non-stationary Stokes and Navier–Stokes problems

AU - Łoś, M.

AU - MUGA URQUIZA, IGNACIO PATRICIO PEDRO

AU - Muñoz-Matute, J.

AU - Paszyński, M.

N1 - Publisher Copyright:
© 2020 Elsevier Ltd
Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2020

Y1 - 2020

N2 - We show that it is possible to obtain a linear computational cost FEM-based solver for non-stationary Stokes and Navier–Stokes equations. Our method employs a technique developed by Guermond and Minev (2011), which consists of singular perturbation plus a splitting scheme. While the time-integration schemes are implicit, we use finite elements to discretize the spatial counterparts. At each time-step, we solve a PDE having weak-derivatives in one direction only (which allows for the linear computational cost), at the expense of handling strong second-order derivatives of the previous time step solution, on the right-hand side of these PDEs. This motivates the use of smooth functions such as B-splines. For high Reynolds numbers, some of these PDEs become unstable. To deal robustly with these instabilities, we propose to use a residual minimization technique. We test our method on problems having manufactured solutions, as well as on the cavity flow problem.

AB - We show that it is possible to obtain a linear computational cost FEM-based solver for non-stationary Stokes and Navier–Stokes equations. Our method employs a technique developed by Guermond and Minev (2011), which consists of singular perturbation plus a splitting scheme. While the time-integration schemes are implicit, we use finite elements to discretize the spatial counterparts. At each time-step, we solve a PDE having weak-derivatives in one direction only (which allows for the linear computational cost), at the expense of handling strong second-order derivatives of the previous time step solution, on the right-hand side of these PDEs. This motivates the use of smooth functions such as B-splines. For high Reynolds numbers, some of these PDEs become unstable. To deal robustly with these instabilities, we propose to use a residual minimization technique. We test our method on problems having manufactured solutions, as well as on the cavity flow problem.

KW - Alternating directions

KW - Isogeometric analysis

KW - Linear computational cost solver

KW - Navier–Stokes problem

KW - Non-stationary Stokes

KW - Residual minimization

UR - http://www.scopus.com/inward/record.url?scp=85097225721&partnerID=8YFLogxK

U2 - 10.1016/j.camwa.2020.11.013

DO - 10.1016/j.camwa.2020.11.013

M3 - Article

AN - SCOPUS:85097225721

JO - Computers and Mathematics with Applications

JF - Computers and Mathematics with Applications

SN - 0898-1221

ER -