Divergence in Natural Convection Simulations with Radiation

Issue

A simulation with radiation and natural convection is either numerically unstable or diverges.

A typical setup configuration for natural convection is to immerse the device in a much larger volume of air, and apply ambient pressure and temperature boundary conditions to the top surface of the volume. The flow enters and leaves the domain only through this surface.

Instead of leaving the side walls adiabatic, many users apply either a fixed temperature or a film coefficient (convection) to the side walls of the air volume.

In certain models that include both natural convection and radiation, numerical instability or even divergence can occur when film coefficient boundary conditions are used on the side walls of the domain. The reason is that they cause a degree of positive feedback for the radiation model, which destabilizes the numerical model.

Solution

Replace the film coefficient boundary conditions on the side walls with fixed temperatures. This often eliminates the problem and produces a stable solution.

Additionally, check your material definitions to ensure that all materials (fluids and solids) have a non-zero emissivity value. (Emissivity “defined” for fluids is actually mapped to all wetted surfaces that are not shared with solid parts.)