EQUATIONS: Remove dependence on nr_function() in SRMHD equations.
Signed-off-by: Grzegorz Kowal <grzegorz@amuncode.org>
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@ -4309,6 +4309,10 @@ module equations
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!
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! using the Newton-Raphson 1Dw iterative method.
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!
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! The derivative dF(W)/dW is
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!
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! dF(W)/dW = 1 - dP/dW + ½ |B|² d|V|²/dW + S² / W³
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!
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! Arguments:
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!
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! mm, en - input coefficients for |M|² and E, respectively;
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@ -4339,8 +4343,8 @@ module equations
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!
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logical :: keep
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integer :: it, cn
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real(kind=8) :: vm, gm, wt
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real(kind=8) :: pr, dpw
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real(kind=8) :: vm, vs, dv, wt, mw
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real(kind=8) :: pr, dp
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real(kind=8) :: f, df, dw
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real(kind=8) :: err
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!
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@ -4365,9 +4369,35 @@ module equations
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!
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do while(keep)
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! calculate F(W) and dF(W)/dW
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! calculate the velocity and its derivative
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!
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call nr_function(mm, bb, mb, en, dn, w, f, df)
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mw = (mb / w)**2
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wt = w + bb
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vv = (mm + (w + wt) * mw) / wt**2
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dv = - 2.0d+00 * (mm + (3.0d+00 * wt + bb**2 / w) * mw) / wt**3
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! calculate 1 - |V|²
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!
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vm = 1.0d+00 - vv
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vs = sqrt(vm)
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! calculate the thermal pressure and its derivative
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!
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! P(W) = (γ - 1)/γ (W - DΓ) (1 - |V|²)
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! dP/dW = (γ - 1)/γ [(1 - D dΓ/dW) (1 - |V|²) - (W - DΓ) d|V|²/dW]
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!
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pr = gammaxi * (w * vm - dn * vs)
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dp = gammaxi * ((1.0d+00 - dn * 0.5d+00 * dv / vm / vs) * vm - (w - dn / vs) * dv)
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! calculate F(W)
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!
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f = w - pr + 0.5d+00 * ((1.0d+00 + vv) * bb - mw) - en
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! calculate dF(W)/dW
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!
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! dF(W)/dW = 1 - dP/dW + ½ |B|² d|V|²/dW + S² / W³
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!
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df = 1.0d+00 - dp + 0.5d+00 * bb * dv + mw / w
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! calculate the increment dW
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!
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@ -4424,104 +4454,6 @@ module equations
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!-------------------------------------------------------------------------------
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!
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end subroutine nr_iterate_srmhd_adi_1dw
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!
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!===============================================================================
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!
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! subroutine NR_FUNCTION:
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! ----------------------
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!
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! Subroutine calculates the value of function
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!
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! F(W) = W - P + ½ [(1 + |V|²) |B|² - S² / W²] - E
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!
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! and its derivative
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!
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! dF(W)/dW = 1 - dP/dW + ½ |B|² d|V|²/dW + S² / W³
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!
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! Arguments:
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!
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! mm, bb, mb, en - input coefficients for |M|², |B|², S, and E,
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! respectively;
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! w - input coefficients W;
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! f, df - output values of the function F(W) and its derivative,
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! respectively;
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!
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! References:
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!
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! Noble, S. C., Gammie, C. F., McKinney, J. C, Del Zanna, L.,
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! "Primitive Variable Solvers for Conservative General Relativistic
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! Magnetohydrodynamics",
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! The Astrophysical Journal, 2006, vol. 641, pp. 626-637
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!
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!===============================================================================
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!
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subroutine nr_function(mm, bb, mb, en, dn, w, f, df)
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! local variables are not implicit by default
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!
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implicit none
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! input/output arguments
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!
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real(kind=8), intent(in) :: mm, bb, mb, en, dn, w
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real(kind=8), intent(out) :: f, df
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! local variables
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!
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real(kind=8) :: mb2, bb2, w2, w3, tm, vv, vm, vs, pr, dv, dg, dp, wt
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!
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!-------------------------------------------------------------------------------
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!
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! prepare some parameters, which do not change
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!
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mb2 = mb * mb
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bb2 = bb * bb
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! prepare W multiplications
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!
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w2 = w * w
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w3 = w * w2
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! calculate the velocity and its derivative
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!
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wt = w + bb
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vv = (mm + (w + wt) * (mb / w)**2) / wt**2
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dv = - 2.0d+00 * (mm + (3.0d+00 * wt + bb**2 / w) * (mb / w)**2) / wt**3
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! calculate 1 - |V|²
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!
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vm = 1.0d+00 - vv
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vs = sqrt(vm)
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! calculate Lorentz factor and its derivative
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!
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! Γ(|V|²) = 1 / sqrt(1 - |V|²)
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! dΓ/dW = ½ Γ³ d|V|²/dW
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!
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dg = 0.5d+00 * dv / vm / vs
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! calculate the thermal pressure and its derivative
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!
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! P(W) = (γ - 1)/γ (W - DΓ) (1 - |V|²)
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! dP/dW = (γ - 1)/γ [(1 - D dΓ/dW) (1 - |V|²) - (W - DΓ) d|V|²/dW]
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!
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tm = w - dn / vs
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pr = gammaxi * tm * vm
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dp = gammaxi * ((1.0d+00 - dn * dg) * vm - tm * dv)
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! calculate F(W)
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!
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f = w - pr + 0.5d+00 * ((1.0d+00 + vv) * bb - mb2 / w2) - en
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! calculate dF(W)/dW
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!
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! dF(W)/dW = 1 - dP/dW + ½ |B|² d|V|²/dW + S² / W³
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!
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df = 1.0d+00 - dp + 0.5d+00 * bb * dv + mb2 / w3
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!-------------------------------------------------------------------------------
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!
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end subroutine nr_function
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!===============================================================================
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!
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