Author:
Wang Yazhou,Xie Ningning,Yin Likun,Zhang Tong,Zhang Xuelin,Mei Shengwei,Xue Xiaodai,Tamma Kumar
Abstract
Purpose
The purpose of this paper is to describe a novel universal error estimator and the adaptive time-stepping process in the generalized single-step single-solve (GS4-1) computational framework, applied for the fluid dynamics with illustrations to incompressible Navier–Stokes equations.
Design/methodology/approach
The proposed error estimator is universal and versatile that it works for the entire subsets of the GS4-1 framework, encompassing the nondissipative Crank–Nicolson method, the most dissipative backward differential formula and anything in between. It is new and novel that the cumbersome design work of error estimation for specific time integration algorithms can be avoided. Regarding the numerical implementation, the local error estimation has a compact representation that it is determined by the time derivative variables at four successive time levels and only involves vector operations, which is simple for numerical implementation. Additionally, the adaptive time-stepping is further illustrated by the proposed error estimator and is used to solve the benchmark problems of lid-driven cavity and flow past a cylinder.
Findings
The proposed computational procedure is capable of eliminating the nonphysical oscillations in GS4-1(1,1)/Crank–Nicolson method; being CPU-efficient in both dissipative and nondissipative schemes with better solution accuracy; and detecting the complex physics and hence selecting a suitable time step according to the user-defined error threshold.
Originality/value
To the best of the authors’ knowledge, for the first time, this study applies the general purpose GS4-1 family of time integration algorithms for transient simulations of incompressible Navier–Stokes equations in fluid dynamics with constant and adaptive time steps via a novel and universal error estimator. The proposed computational framework is simple for numerical implementation and the time step selection based on the proposed error estimation is efficient, benefiting to the computational expense for transient simulations.
Subject
Applied Mathematics,Computer Science Applications,Mechanical Engineering,Mechanics of Materials
Reference33 articles.
1. Investigation of the Oldroyd model as a generalized incompressible Navier–Stokes equation via the interpolating stabilized element free Galerkin technique;Applied Numerical Mathematics,2020
2. Adaptive asynchronous time-stepping, stopping criteria, and a posteriori error estimates for fixed-stress iterative schemes for coupled poromechanics problems;Journal of Computational and Applied Mathematics,2020
3. Crank–Nicolson finite difference method for two-dimensional diffusion with an integral condition;Applied Mathematics and Computation,2001
4. The method of variably scaled radial kernels for solving two-dimensional magnetohydrodynamic (MHD) equations using two discretizations: the Crank–Nicolson scheme and the method of lines (MOL);Computers and Mathematics with Applications,2015
5. The boundary knot method for the solution of two-dimensional advection reaction-diffusion and brusselator equations;International Journal of Numerical Methods for Heat and Fluid Flow,2020
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