Abstract
| Original language | English |
|---|---|
| Pages (from-to) | 1051-1071 |
| Number of pages | 21 |
| Journal | SIAM Journal on Numerical Analysis |
| Volume | 34 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - 1997 |
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Keywords
- Sequential regularization method
- Navier-Stokes equations
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A sequential regularization method for time-dependent incompressible Navier--Stokes equations. / Lin, Ping.
In: SIAM Journal on Numerical Analysis, Vol. 34, No. 3, 1997, p. 1051-1071.Research output: Contribution to journal › Article
TY - JOUR
T1 - A sequential regularization method for time-dependent incompressible Navier--Stokes equations
AU - Lin, Ping
N1 - © 1997 Society for Industrial and Applied Mathematics
PY - 1997
Y1 - 1997
N2 - The objective of the paper is to present a method, called the sequential regularization method (SRM), for the nonstationary incompressible Navier--Stokes equations from the viewpoint of regularization of differential-algebraic equations (DAEs), and to provide a way to apply a DAE method to partial differential-algebraic equations (PDAEs). The SRM is a functional iterative procedure. It is proved that its convergence rate is $O(\epsilon^m)$, where $m$ is the number of the SRM iterations and $\epsilon$ is the regularization parameter. The discretization and implementation issues of the method are considered. In particular, a simple explicit-difference scheme is analyzed and its stability is proved under the usual step-size condition of explicit schemes. It appears that the SRM formulation is new in the Navier--Stokes context. Unlike other regularizations or pseudocompressibility methods in the Navier--Stokes context, the regularization parameter $\epsilon$ in the SRM need not be very small and the regularized problem in the sequence may be essentially nonstiff in time direction for any $\epsilon$. Hence the stability condition is independent of $\epsilon$ even for explicit time discretization. Numerical experiments are given to verify our theoretical results.
AB - The objective of the paper is to present a method, called the sequential regularization method (SRM), for the nonstationary incompressible Navier--Stokes equations from the viewpoint of regularization of differential-algebraic equations (DAEs), and to provide a way to apply a DAE method to partial differential-algebraic equations (PDAEs). The SRM is a functional iterative procedure. It is proved that its convergence rate is $O(\epsilon^m)$, where $m$ is the number of the SRM iterations and $\epsilon$ is the regularization parameter. The discretization and implementation issues of the method are considered. In particular, a simple explicit-difference scheme is analyzed and its stability is proved under the usual step-size condition of explicit schemes. It appears that the SRM formulation is new in the Navier--Stokes context. Unlike other regularizations or pseudocompressibility methods in the Navier--Stokes context, the regularization parameter $\epsilon$ in the SRM need not be very small and the regularized problem in the sequence may be essentially nonstiff in time direction for any $\epsilon$. Hence the stability condition is independent of $\epsilon$ even for explicit time discretization. Numerical experiments are given to verify our theoretical results.
KW - Sequential regularization method
KW - Navier-Stokes equations
U2 - 10.1137/S0036142994270521
DO - 10.1137/S0036142994270521
M3 - Article
VL - 34
SP - 1051
EP - 1071
JO - SIAM Journal on Numerical Analysis
JF - SIAM Journal on Numerical Analysis
SN - 0036-1429
IS - 3
ER -