Time Relaxation with Iterative Modified Lavrentiev Regularization

TL;DR

This paper introduces a new time relaxation model using iterative modified Lavrentiev regularization to improve the accuracy and efficiency of simulations by better controlling unresolved fluctuations and solution scales.

Contribution

It presents a novel time relaxation approach combined with iterative modified Lavrentiev regularization, providing insights into parameter selection and improved approximation with fewer computational steps.

Findings

The relaxation term accelerates the decay of unresolved fluctuations.

The model offers better approximation with fewer de-convolution steps.

Guidelines for choosing the relaxation parameter are provided.

Abstract

A new time relaxation model with iterative modified Lavrentiev regularization method is studied. The aim of the relaxation term is to drive the unresolved fluctuations in a computational simulation to zero exponentially faster by an appropriate and often problem-dependent choice of its time relaxation parameter; together with iterative modified Lavrentiev regularization, the model will give a better approximation through de-convolution with fewer steps to compute. The goal of this paper herein is to understand how this time relaxation term acts to truncate solution scales and to use this understanding to give some helpful insight into parameter selection.