On the area of optimal parameters choice for the numerical method of non-stationary hydrodynamics problem with feature

TL;DR

This paper investigates the optimal parameter selection for numerical solutions of non-stationary Navier-Stokes equations, focusing on how parameters depend on domain geometry, input data, and discretization methods like Runge-Kutta.

Contribution

It experimentally determines optimal parameters in the Navier-Stokes numerical method based on domain features, input data, and finite element discretization, including Runge-Kutta schemes.

Findings

Optimal parameters depend on domain geometry and input data.

Optimal parameter regions vary with incoming flow angles.

Finite element and Runge-Kutta methods effectively discretize the problem.

Abstract

For an approximate solution of the non-stationary nonlinear Navier-Stokes equations for the flow of an incompressible viscous fluid, depending on the set of input data and the geometry of the domain, the area of optimal parameters in the variables $\nu$ and $\nu^{\ast}$ is experimentally determined depending on $\delta$ included in the definition of the $R_{\nu}$-generalized solution of the problem and the degree of the weight function in the basis of the finite element method. To discretize the problem in time, the Runge-Kutta methods of the first and second orders were used. The areas of optimal parameters for various values of the incoming angles are established.