submodule (mod_matrix_manager) smod_hall_matrix implicit none contains module procedure add_hall_bmatrix_terms real(dp) :: eps, deps real(dp) :: rho, drho real(dp) :: eta_H, eta_e real(dp) :: WVop type(matrix_elements_t) :: elements eps = grid%get_eps(x_gauss) deps = grid%get_deps() rho = background%density%rho0(x_gauss) drho = background%density%drho0(x_gauss) eta_H = physics%hall%hallfactor(x_gauss) eta_e = physics%hall%inertiafactor(x_gauss) WVop = k2**2 / eps + eps * k3**2 elements = new_matrix_elements(state_vector=settings%get_state_vector()) ! ==================== Quadratic * Cubic ==================== call elements%add(eta_H, "a1", "v1", spline1=h_quad, spline2=h_cubic) ! ==================== Cubic * Quadratic ==================== call elements%add(eta_H * eps, "a2", "v2", spline1=h_cubic, spline2=h_quad) call elements%add(eta_H, "a3", "v3", spline1=h_cubic, spline2=h_quad) if (settings%physics%hall%has_electron_inertia()) then ! ==================== Quadratic * Quadratic ==================== call elements%add(eta_e * WVop / rho, "a1", "a1", spline1=h_quad, spline2=h_quad) ! ==================== Quadratic * dCubic ==================== call elements%add( & -eta_e * k2 / (eps * rho), "a1", "a2", spline1=h_quad, spline2=dh_cubic & ) call elements%add( & -eta_e * eps * k3 / rho, "a1", "a3", spline1=h_quad, spline2=dh_cubic & ) ! ==================== Cubic * Quadratic ==================== call elements%add( & -eta_e * k2 * (deps / (eps * rho) - drho / rho**2), & "a2", & "a1", & spline1=h_cubic, & spline2=h_quad & ) call elements%add( & eta_e * drho * eps * k3 / rho**2, "a3", "a1", spline1=h_cubic, spline2=h_quad & ) ! ==================== dCubic * Quadratic ==================== call elements%add(-eta_e * k2 / rho, "a2", "a1", spline1=dh_cubic, spline2=h_quad) call elements%add( & -eta_e * eps * k3 / rho, "a3", "a1", spline1=dh_cubic, spline2=h_quad & ) ! ==================== Cubic * Cubic ==================== call elements%add( & eta_e * k3**2 / rho, "a2", "a2", spline1=h_cubic, spline2=h_cubic & ) call elements%add( & -eta_e * k2 * k3 / rho, "a2", "a3", spline1=h_cubic, spline2=h_cubic & ) call elements%add( & -eta_e * k2 * k3 / (eps * rho), "a3", "a2", spline1=h_cubic, spline2=h_cubic & ) call elements%add( & eta_e * k2**2 / (eps * rho), "a3", "a3", spline1=h_cubic, spline2=h_cubic & ) ! ==================== Cubic * dCubic ==================== call elements%add( & eta_e * (deps / (eps * rho) - drho / rho**2), & "a2", & "a2", & spline1=h_cubic, & spline2=dh_cubic & ) call elements%add( & -eta_e * eps * drho / rho**2, "a3", "a3", spline1=h_cubic, spline2=dh_cubic & ) ! ==================== dCubic * dCubic ==================== call elements%add(eta_e / rho, "a2", "a2", spline1=dh_cubic, spline2=dh_cubic) call elements%add( & eta_e * eps / rho, "a3", "a3", spline1=dh_cubic, spline2=dh_cubic & ) end if call add_to_quadblock(quadblock, elements, weight, settings%dims) call elements%delete() end procedure add_hall_bmatrix_terms module procedure add_hall_matrix_terms real(dp) :: eps, deps real(dp) :: v01, v02, v03, dv01, dv02, dv03, ddv01, ddv02, ddv03 real(dp) :: rho, drho, T0, dT0, B01, B02, B03, dB02, dB03 real(dp) :: drB02, dB02_r, Fop_plus, Gop_plus, Gop_min, WVop real(dp) :: eta_H, mu, efrac type(matrix_elements_t) :: elements logical :: has_viscosity eps = grid%get_eps(x_gauss) deps = grid%get_deps() v01 = background%velocity%v01(x_gauss) v02 = background%velocity%v02(x_gauss) v03 = background%velocity%v03(x_gauss) dv01 = background%velocity%dv01(x_gauss) dv02 = background%velocity%dv02(x_gauss) dv03 = background%velocity%dv03(x_gauss) ddv01 = background%velocity%ddv01(x_gauss) ddv02 = background%velocity%ddv02(x_gauss) ddv03 = background%velocity%ddv03(x_gauss) rho = background%density%rho0(x_gauss) drho = background%density%drho0(x_gauss) T0 = background%temperature%T0(x_gauss) dT0 = background%temperature%dT0(x_gauss) B01 = background%magnetic%B01(x_gauss) B02 = background%magnetic%B02(x_gauss) dB02 = background%magnetic%dB02(x_gauss) B03 = background%magnetic%B03(x_gauss) dB03 = background%magnetic%dB03(x_gauss) ! Calculate derivatives eps*B02, B02/eps drB02 = deps * B02 + eps * dB02 dB02_r = dB02 / eps - B02 * deps / eps**2 Fop_plus = k2 * B02 / eps + k3 * B03 Gop_plus = k3 * B02 + k2 * B03 / eps Gop_min = k3 * B02 - k2 * B03 / eps WVop = k2**2 / eps + eps * k3**2 eta_H = physics%hall%hallfactor(x_gauss) mu = settings%physics%viscosity%get_viscosity_value() efrac = settings%physics%hall%get_electron_fraction() elements = new_matrix_elements(state_vector=settings%get_state_vector()) has_viscosity = settings%physics%viscosity%is_enabled() ! Hall by substitution of the momentum equation ! ==================== Quadratic * Cubic ==================== call elements%add( & eta_H * (k2 * v02 / eps + k3 * v03), & "a1", & "v1", & spline1=h_quad, & spline2=h_cubic & ) ! ==================== Quadratic * Quadratic ==================== call elements%add( & -eta_H * (1.0d0 - efrac) * dT0 / rho, & "a1", & "rho", & spline1=h_quad, & spline2=h_quad & ) call elements%add( & -2.0d0 * eta_H * deps * v02, "a1", "v2", spline1=h_quad, spline2=h_quad & ) call elements%add( & eta_H * (1.0d0 - efrac) * drho / rho, & "a1", & "T", & spline1=h_quad, & spline2=h_quad & ) ! ==================== Cubic * Cubic ==================== call elements%add( & -eta_H * (dv02 - v02 * deps / eps), & "a2", & "v1", & spline1=h_cubic, & spline2=h_cubic & ) call elements%add(-eta_H * dv03, "a3", "v1", spline1=h_cubic, spline2=h_cubic) ! ==================== Cubic * Quadratic ==================== call elements%add( & eta_H * (k2 * v02 + eps * k3 * v03), & "a2", & "v2", & spline1=h_cubic, & spline2=h_quad & ) call elements%add( & eta_H * (k2 * v02 / eps + k3 * v03), & "a3", & "v3", & spline1=h_cubic, & spline2=h_quad & ) ! elements below are only relevant when viscosity is included if (.not. has_viscosity) return ! ==================== Quadratic * Cubic ==================== call elements%add( & -eta_H * ic * mu * ( & (drho / rho + 1.0d0 / eps) * deps / eps + (k2 / eps)**2 + k3**2 & ) / rho, & "a1", & "v1", & spline1=h_quad, & spline2=h_cubic & ) ! ==================== Quadratic * dCubic ==================== call elements%add( & eta_H * ic * mu * (4.0d0 * drho / rho - deps / eps) / (3.0d0 * rho), & "a1", & "v1", & spline1=h_quad, & spline2=dh_cubic & ) ! ==================== dQuadratic * Cubic ==================== call elements%add( & eta_H * ic * mu * deps / (eps * rho), & "a1", & "v1", & spline1=dh_quad, & spline2=h_cubic & ) ! ==================== dQuadratic * dCubic ==================== call elements%add( & -4.0d0 * eta_H * ic * mu / (3.0d0 * rho), & "a1", & "v1", & spline1=dh_quad, & spline2=dh_cubic & ) ! ==================== Quadratic * Quadratic ==================== call elements%add( & eta_H * mu * 4.0d0 * (ddv01 + deps * (dv01 - v01 / eps) / eps) & / (3.0d0 * rho**2), & "a1", & "rho", & spline1=h_quad, & spline2=h_quad & ) call elements%add( & 7.0d0 * eta_H * ic * mu * deps * k2 / (3.0d0 * eps * rho), & "a1", & "v2", & spline1=h_quad, & spline2=h_quad & ) call elements%add( & eta_H * ic * mu * k3 * deps / (3.0d0 * eps * rho), & "a1", & "v3", & spline1=h_quad, & spline2=h_quad & ) ! ==================== Quadratic * dQuadratic ==================== call elements%add( & -eta_H * ic * mu * k2 / (3.0d0 * rho), & "a1", & "v2", & spline1=h_quad, & spline2=dh_quad & ) call elements%add( & -eta_H * ic * mu * k3 / (3.0d0 * rho), & "a1", & "v3", & spline1=h_quad, & spline2=dh_quad & ) ! ==================== Cubic * Cubic ==================== call elements%add( & 2.0d0 * eta_H * ic * mu * k2 * deps / (eps**2 * rho), & "a2", & "v1", & spline1=h_cubic, & spline2=h_cubic & ) ! ==================== Cubic * dCubic ==================== call elements%add( & eta_H * ic * mu * k2 / (3.0d0 * eps * rho), & "a2", & "v1", & spline1=h_cubic, & spline2=dh_cubic & ) call elements%add( & eta_H * ic * mu * k3 / (3.0d0 * rho), & "a3", & "v1", & spline1=h_cubic, & spline2=dh_cubic & ) ! ==================== Cubic * Quadratic ==================== call elements%add( & -ic * eta_H * mu * (ddv02 + deps * (dv02 - v02 / eps) / eps) / rho**2, & "a2", & "rho", & spline1=h_cubic, & spline2=h_quad & ) call elements%add( & -eta_H * ic * mu * ( & 4.0d0 * k2**2 / (3.0d0 * eps) + eps * k3**2 + deps / eps & ) / rho, & "a2", & "v2", & spline1=h_cubic, & spline2=h_quad & ) call elements%add( & -eta_H * ic * mu * k2 * k3 / (3.0d0 * eps * rho), & "a2", & "v3", & spline1=h_cubic, & spline2=h_quad & ) call elements%add( & -ic * eta_H * mu * (ddv03 + deps * dv03 / eps) / rho**2, & "a3", & "rho", & spline1=h_cubic, & spline2=h_quad & ) call elements%add( & -eta_H * ic * mu * k2 * k3 / (3.0d0 * rho), & "a3", & "v2", & spline1=h_cubic, & spline2=h_quad & ) call elements%add( & -eta_H * ic * mu * ( & (k2 / eps)**2 + 4.0d0 * k3**2 / 3.0d0 + drho * deps / (eps * rho) & ) / rho, & "a3", & "v3", & spline1=h_cubic, & spline2=h_quad & ) ! ==================== Cubic * dQuadratic ==================== call elements%add( & eta_H * ic * mu * eps * drho / rho**2, & "a2", & "v2", & spline1=h_cubic, & spline2=dh_quad & ) call elements%add( & eta_H * ic * mu * drho / rho**2, & "a3", & "v3", & spline1=h_cubic, & spline2=dh_quad & ) ! ==================== dCubic * dQuadratic ==================== call elements%add( & -eta_H * ic * mu * eps / rho, "a2", "v2", spline1=dh_cubic, spline2=dh_quad & ) call elements%add( & -eta_H * ic * mu / rho, "a3", "v3", spline1=dh_cubic, spline2=dh_quad & ) ! ==================== dCubic * Quadratic ==================== call elements%add( & eta_H * ic * mu * deps / (eps * rho), & "a3", & "v3", & spline1=dh_cubic, & spline2=h_quad & ) call add_to_quadblock(quadblock, elements, weight, settings%dims) call elements%delete() end procedure add_hall_matrix_terms end submodule smod_hall_matrix