scalar_transport

Note

We currently only support a linear formulation.

solver	Scalar transport solver configuration.
spatial	Definitions of the spatial discretizations for the scalar transport equation.
time	Definitions of the temporal discretizations for the scalar transport equation.
riemann_solver	Definitions of riemann solvers for a scalar transport equation.
config	Definitions of boundary/domain conditions for a scalar transport equation.

Scalar transport equation

A transport equation expresses a conservation principle by describing how a physical quantity \(\phi\) evolves in space and time due to the combined effects of convection and diffusion. A general form of this process is modeled by the (linear and scalar) convection–diffusion equation:

\[\begin{align*} \frac{\partial \phi}{\partial t} + \nabla \cdot (\vec{b}\phi) - \nabla \cdot (\kappa \nabla \phi) = 0, \end{align*}\]

where \(\vec{b}\) is the advecting velocity field (possibly space-dependent) and \(\kappa\) is the diffusivity coefficient. Note, the dimension of \(\vec{b}\) is deduced from the spatial dimension of the input grid.

note:

A pure convection equation can be solved, by setting is_inviscid() to False.

Examples

• Scalar wave equation in 1D
• Rotation of a Gaussian hill