solver¶

Functions to solve the diffusion equation

solver.A(P)¶: Power-law scheme, Patankar eq. 5.34

solver.F_upwind(F)¶: Upwinding scheme

solver.apparent_heat(z_edges, Z_P, nt, dt, Gamma_P, phi_0, nz_P, nz_fv, phi_s, mix_rho, c_vol, LWC, mass_sol, dz, ICT, rho_firn, iii=0)¶

transient 1-d diffusion finite volume method

This is for standard heat (no liquid water), isotope, and air diffusion. If there is liquid water is should use the enthalpy solver.

Parameters:	z_edges – Z_P – nt – dt – Gamma_P – phi_0 – nz_P – nz_fv – phi_s –
Return phi_t:

solver.solver(a_U, a_D, a_P, b)¶

function for solving matrix problem

Parameters:	a_U – a_D – a_P – b –
Return phi_t:

solver.transient_solve_EN(z_edges, Z_P, nt, dt, Gamma_P, phi_0, nz_P, nz_fv, phi_s, mix_rho, c_vol, LWC, mass_sol, dz, ICT, rho_firn, iii=0)¶

transient 1-d diffusion finite volume method for enthalpy

This is for heat diffusion when there is liquid water present. It uses a source term for the latent heat associated with the liquid water.

Parameters:	z_edges – Z_P – nt – number of iterations; depricated (now uses while loop) dt – time step size Gamma_P – phi_0 – temperature profile [C] nz_P – nz_fv – phi_s – surface temperature [C]

:param g_liq :param c_vol: [J/m3/K] ‘volume-averaged specific heat of mixture’, or rho * cp. (so really heat capacity)

Return phi_t:

The source terms S_P and S_C come from the linearization described in Voller and Swaminathan, 1991, equations 31 and 32. and Voller, Swaminathan, and Thomas, 1990, equation 61

solver.transient_solve_TR(z_edges, Z_P, nt, dt, Gamma_P, phi_0, nz_P, nz_fv, phi_s, tot_rho, c_vol, airdict=None)¶

transient 1-d diffusion finite volume method

This is for standard heat (no liquid water), isotope, and air diffusion. If there is liquid water is should use the enthalpy solver.

Parameters:	z_edges – Z_P – nt – dt – Gamma_P – phi_0 – nz_P – nz_fv – phi_s –
Return phi_t:

solver.w(airdict, z_edges, rho_edges, Z_P, dZ)¶: Function for downward advection of air and also calculates total air content.