7.2. Finite Volumes

7.2.1. Classes

daeHRUpwindSchemeEquation

class daeHRUpwindSchemeEquation(variable, domain, phi, r_epsilon=1e-10, reversedFlow=False)

supported_flux_limiters = [<function daeHRUpwindSchemeEquation.Phi_HCUS>, <function daeHRUpwindSchemeEquation.Phi_HQUICK>, <function daeHRUpwindSchemeEquation.Phi_Koren>, <function daeHRUpwindSchemeEquation.Phi_monotinized_central>, <function daeHRUpwindSchemeEquation.Phi_minmod>, <function daeHRUpwindSchemeEquation.Phi_Osher>, <function daeHRUpwindSchemeEquation.Phi_ospre>, <function daeHRUpwindSchemeEquation.Phi_smart>, <function daeHRUpwindSchemeEquation.Phi_superbee>, <function daeHRUpwindSchemeEquation.Phi_Sweby>, <function daeHRUpwindSchemeEquation.Phi_UMIST>, <function daeHRUpwindSchemeEquation.Phi_vanAlbada1>, <function daeHRUpwindSchemeEquation.Phi_vanAlbada2>, <function daeHRUpwindSchemeEquation.Phi_vanLeer>, <function daeHRUpwindSchemeEquation.Phi_vanLeer_minmod>]

__init__(variable, domain, phi, r_epsilon=1e-10, reversedFlow=False)

dc_dt(i, variable=None)

Accumulation term in the cell-centered finite-volume discretisation:

\(\int_{\Omega_i} {\partial c_i \over \partial t} dx\)

dc_dx(i, S=None, variable=None)

Convection term in the cell-centered finite-volume discretisation:

\(c_{i + {1 \over 2}} - c_{i - {1 \over 2}}\).

Cell-face state \(c_{i+{1 \over 2}}\) is given as:

\({c}_{i + {1 \over 2}} = c_i + \phi \left( r_{i + {1 \over 2}} \right) \left( c_i - c_{i-1} \right)\)

where \(\phi\) is the flux limiter function and \(r_{i + {1 \over 2}}\) the upwind ratio of consecutive solution gradients:

\(r_{i + {1 \over 2}} = {{c_{i+1} - c_{i} + \epsilon} \over {c_{i} - c_{i-1} + \epsilon}}\).

If the source term integral \(S= {1 \over u} \int_{\Omega_i} s(x) dx\) is not None then the convection term is given as: \((c-S)_{i + {1 \over 2}} - (c-S)_{i - {1 \over 2}}\).

d2c_dx2(i, variable=None)

Diffusion term in the cell-centered finite-volume discretisation:

\(\left( \partial c_i \over \partial x \right)_{i + {1 \over 2}} - \left( \partial c_i \over \partial x \right)_{i - {1 \over 2}}\)

source(s, i)

Source term in the cell-centered finite-volume discretisation:

\(\int_{\Omega_i} s(x) dx\)