daeHRUpwindSchemeEquation |
daeHRUpwindSchemeEquation(variable, domain, phi, r_epsilon=1e-10, reversedFlow=False)[source]¶Bases: object
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>]¶dc_dt(i, variable=None)[source]¶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)[source]¶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:
\((c-S)_{i + {1 \over 2}} - (c-S)_{i - {1 \over 2}}\).