Convection of a gaussian hill problem

Kratos version: 8.0

Source files: source

Case Specification

This example is taken from [Kuzmin, D. (2010). Unsteady Transport Problems. In A Guide to Numerical Methods for Transport Equations (pp. 180–184). Section 4.4.6.3].

We solve the transient convection equation $\frac{\partial \phi}{\partial t} + v \cdot \nabla \phi + \phi \nabla \cdot v - \nabla \cdot k \nabla \phi = f$ , where null diffusivity $k$ is considered. Specific initial conditions are set, we refer to the above reference for further details.

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 the results we obtain are consistent with the reference [Donea, J., & Huerta, A. (2003). Finite Element Methods for Flow Problems. Section 5.6.1]. Moreover, we observe the solution peak is not being diffused in the domain, as one should expect for a pure-convection problem.