# solver

Functions to solve the diffusion equation

`solver.``A`(P)

  Power-law scheme, Patankar eq. 5.34

`solver.``F_upwind`(F)

  Upwinding scheme

`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, tot_rho, c_vol, g_liq, deltaH)

  transient 1-d diffusion finite volume method for enthalpy

  Parameters

    - z_edges –

    - Z_P –

    - nt –

    - dt –

    - Gamma_P –

    - phi_0 –

    - nz_P –

    - nz_fv –

    - phi_s –

  :param g_liq

  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 :param z_edges: :param Z_P: :param nt: :param dt: :param Gamma_P: :param phi_0: :param nz_P: :param nz_fv: :param 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.