Defect-Deferred Correction Method Based on a Subgrid Artificial Viscosity Model for Fluid-Fluid Interaction

TL;DR

This paper introduces a defect-deferred correction method with a subgrid artificial viscosity model to improve accuracy and stability in fluid-fluid interaction simulations, effectively balancing dissipation and precision.

Contribution

It presents a novel defect-deferred correction approach that incorporates a subgrid artificial viscosity model, enhancing both temporal and spatial accuracy for nonlinear interface problems.

Findings

The method achieves higher accuracy in fluid-fluid interaction simulations.

Stability of the algorithm is confirmed through analytical and numerical analysis.

Artificial viscosity effectively controls fluctuations without compromising accuracy.

Abstract

A defect-deferred correction method, increasing both temporal and spatial accuracy, for fluid-fluid interaction problem with nonlinear interface condition is considered by geometric averaging of the previous two-time levels. In the defect step, an artificial viscosity is added only on the fluctuations in the velocity gradient by removing this effect on a coarse mesh. The dissipative influence of the artificial viscosity is further eliminated in the correction step while gaining additional temporal accuracy at the same time. The stability and accuracy analyses of the resulting algorithm are investigated both analytically and numerically.