Discontinuous Galerkin code to solve hyperbolic PDEs
Adrien Crovato, 2021
dg-flo is a python code that can solve one-dimensional hyperbolic partial differential equations of the form
dU/dt + dF(U)/dx + S(x) = 0
where U is the vector of unknowns, F(U) is the vector of convective fluxes and S(x) is a vector of source terms.
Examples of formulation already implemented in dg-flo:
-
Linear advection equation
du/dt + a du/dx = 0 -
Burger's equation
du/dt + u du/dx = 0 -
Euler equations
[rho] [ rho u ] [ 0 ]
d[ u ] / dt + d[rho u^2 + p] / dx = [ 0 ]
[ E ] [ (E + p) u ] [ 0 ]
Sod's shock tube
- Saint-Venant (shallow water) equations
[ h ] [ h u ] [ 0 ] [ 0 ]
d[ ] / dt + d[ ] / dx + [ ] = [ ]
[ u ] [ g h + u^2 / 2 ] [ g dz/dx ] [ 0 ]
Tsunami propagation
