pyro.viscous_burgers package
The pyro viscous burgers solver. This implements a second-order, unsplit method for viscous burgers equations.
Subpackages
Submodules
pyro.viscous_burgers.interface module
- pyro.viscous_burgers.interface.apply_diffusion_corrections(grid, dt, eps, u, v, u_xl, u_xr, u_yl, u_yr, v_xl, v_xr, v_yl, v_yr)[source]
Apply diffusion correction term to the interface state
\[u_t + u u_x + v u_y = eps (u_xx + u_yy) v_t + u v_x + v v_y = eps (v_xx + v_yy)\]We use a second-order (piecewise linear) unsplit Godunov method (following Colella 1990).
Our convection is that the fluxes are going to be defined on the left edge of the computational zones:
| | | | | | | | -+------+------+------+------+------+------+-- | i-1 | i | i+1 | a_l,i a_r,i a_l,i+1
a_r,i and a_l,i+1 are computed using the information in zone i,j.
- Parameters:
- gridGrid2d
The grid object
- dtfloat
The timestep
- epsfloat
The viscosity
- u_xl, u_xrndarray ndarray
left and right states of x-velocity in x-interface.
- u_yl, u_yrndarray ndarray
left and right states of x-velocity in y-interface.
- v_xl, v_xrndarray ndarray
left and right states of y-velocity in x-interface.
- v_yl, u_yrndarray ndarray
left and right states of y-velocity in y-interface.
- Returns:
- outndarray, ndarray, ndarray, ndarray, ndarray, ndarray, ndarray, ndarray
unsplit predictions of the left and right states of u and v on both the x- and y-interfaces along with diffusion correction terms.
- pyro.viscous_burgers.interface.diffuse(my_data, rp, dt, scalar_name, A)[source]
A routine to solve the Helmhotlz equation with constant coefficient and update the state.
(a + b lap) phi = f
using Crank-Nicolson discretization with multigrid V-cycle.
- Parameters:
- my_dataCellCenterData2d object
The data object containing the grid and advective scalar that we are advecting.
- rpRuntimeParameters object
The runtime parameters for the simulation
- dtfloat
The timestep we are advancing through.
- scalar_namestr
The name of the variable contained in my_data that we are advecting
- A: ndarray
The advective source term for diffusion
- Returns:
- outndarray (solution of the Helmholtz equation)
pyro.viscous_burgers.simulation module
- class pyro.viscous_burgers.simulation.Simulation(solver_name, problem_name, rp, timers=None, data_class=<class 'pyro.mesh.patch.CellCenterData2d'>)[source]
Bases:
Simulation