A rotational velocity‐correction projection method for the Kelvin–Voigt viscoelastic fluid equations

Abstract

In this paper, a semi‐discrete rotational velocity‐correction projection method is proposed to solve the Kelvin–Voigt viscoelastic fluid equations. In this method, the rotational velocity‐correction projection method can preserve the divergence free of the velocity , and the nonlinear equation was linearized. Then, the unconditional stability and optimal convergence order will be provided by the numerical analysis. Finally, our analysis are confirmed by some numerical results, and the algorithm is effective.

Editorial of the special issue on modelling, analysis, and applications

“…Primal and dual formulations of singular autonomous systems of three different types of fractional‐order differential equations are visited and discussed in another study [25]. Solving the Kelvin‐Voigt viscoelastic fluid equations is the topic of another paper [26], in which a semi‐discrete rotational velocity‐correction projection method is applied. The theoretical analysis is confirmed by numerical results, showing the algorithm's effectiveness.…”