Refactorization of a variable step, unconditionally stable method of Dahlquist, Liniger and Nevanlinna

08/20/2021
by   William Layton, et al.
0

The one-leg, two-step time-stepping scheme proposed by Dahlquist, Liniger and Nevanlinna has clear advantages in complex, stiff numerical simulations: unconditional G-stability for variable time-steps and second-order accuracy. Yet it has been underutilized due, partially, to its complexity of direct implementation. We prove herein that this method is equivalent to the backward Euler method with pre- and post arithmetic steps added. This refactorization eases implementation in complex, possibly legacy codes. The realization we develop reduces complexity, including cognitive complexity and increases accuracy over both first order methods and constant time steps second order methods.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
06/19/2019

Numerical analysis of an efficient second order time filtered backward Euler method for MHD equations

The present work is devoted to introduce the backward Euler based modula...
research
10/08/2021

Walking into the complex plane to 'order' better time integrators

Most numerical methods for time integration use real time steps. Complex...
research
01/23/2020

Analysis of the variable step method of Dahlquist, Liniger and Nevanlinna for fluid flow

The two-step time discretization proposed by Dahlquist, Liniger and Neva...
research
12/02/2020

Proper Selection of Obreshkov-Like Numerical Integrators Used as Numerical Differentiators

Criteria for Obreshkov-like numerical integrators to be used as numerica...
research
06/09/2021

On the Analysis of the Second Order Time Filtered Backward Euler Method for the EMAC formulation of Navier-Stokes Equations

This paper considers the backward Euler based linear time filtering meth...
research
07/18/2019

Doubly-Adaptive Artificial Compression Methods for Incompressible Flow

This report presents adaptive artificial compression methods in which th...

Please sign up or login with your details

Forgot password? Click here to reset