Limitation of Finite Difference Scheme in Electroconvection with Unipolar Charge Injection: A base-state Analysis

TL;DR

This paper analyzes the limitations of finite difference schemes in modeling electroconvection with unipolar charge injection, focusing on the base state and boundary layer resolution.

Contribution

It provides an analytical derivation of the boundary layer near the anode and discusses the computational challenges in accurately resolving it.

Findings

Finite difference schemes require fine grids to resolve boundary layers.

Analytical boundary layer expressions aid in improving numerical accuracy.

Limitations of finite difference methods impact electroconvection modeling accuracy.

Abstract

The 1D hydrostatic base state of electroconvection driven by unipolar charge injection between two parallel electrodes is investigated using a finite difference method. A boundary layer near the anode surface is derived analytically. The computational grid is required to resolve this boundary layer to maintain high order accuracy.