Transient rotating pulse problem

Kratos version: 8.0

Source files: source

Case Specification

This example is taken from [Donea, J., & Huerta, A. (2003). Finite Element Methods for Flow Problems. Section 5.6.2]. We solve the transient convection diffusion equation $\frac{\partial \phi}{\partial t} + v \cdot \nabla \phi + \phi \nabla \cdot v - \nabla \cdot k \nabla \phi = f$ , where null Dirichlet boundary condition and null initial conditions are set. We refer to the above reference for further details.

Citing [Donea, J., & Huerta, A. (2003). Finite Element Methods for Flow Problems. Section 5.6.2], this problem requires accurate transport of the unknown and boundary layers appear in the solution due to the Dirichlet boundary conditions. Therefore, high-order time-stepping schemes and stabilized formulations are needed in order to obtain an accurate solution.

The problem is solved exploiting the Runge-Kutta 4 time integration explicit method, and it can be run with four different stabilizations:

quasi-static algebraic subgrid scale (QSASGS)
quasi-static orthogonal subgrid scale (QSOSS)
dynamic algebraic subgrid scale (DASGS)
dynamic orthogonal subgrid scale (DOSS)

Results

We present the temporal evolution of $\phi$ for the DOSS case.

temperature

We can observe that the results we obtain are consistent with the reference [Donea, J., & Huerta, A. (2003). Finite Element Methods for Flow Problems. Section 5.6.2].