PLUTO Test Problems
4.4-patch2
|
Propagation of a conduction front. More...
Functions | |
void | Analysis (const Data *d, Grid *grid) |
void | InitDomain (Data *d, Grid *grid) |
The problem sets the initial condition for a propagating conduction front for which an analytical solution exists (Reale 1995).
The equation
has the solution
where
is the integral over the whole space, and
is the gamma function.
The setup is built to compare the numerical solution with the analytical one.
In order to solve just the internal energy equation, we force the velocity to be zero using the internal boundary. We then deal with the internal energy equation (in cgs units) in presence of conduction,
where is the gas internal energy (in cgs units),
is the temperature (in K),
is the plasma thermal conductivity (in cgs units): The previous equation can be written in terms of the temperature variable only using
where (
is employed in 1D) is the plasma number density,
while
In code (non-dimensional) units, we adopt ,
and therefore Eq. (eq:internal_energy}) is solved as
Values with a tilde are dimensionless. Note that the reference velocity and temperature are computed directly from :
.
Configurations (EXPLICIT
, STS
, RKL
):
References:
void Analysis | ( | const Data * | d, |
Grid * | grid | ||
) |
Generate Analytical solution