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EQUATIONS: Correct comments in SRHD variable solvers.

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Signed-off-by: Grzegorz Kowal <grzegorz@amuncode.org>
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Grzegorz Kowal 2015-02-20 09:42:33 -02:00
parent 1b37e6dc47
commit d30f5a6f20
1 changed files with 30 additions and 27 deletions
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57
src/equations.F90
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@ -3533,7 +3533,7 @@ module equations
!
! mm, en - input coefficients for |M|² and E, respectively;
! bb, bm - input coefficients for |B|² and B.M, respectively;
! w, vv - input/output coefficients W and |V|²;
! w, vv - input/output coefficients W and |v|²;
!
! References:
!
@ -3616,15 +3616,15 @@ module equations
!
do while(keep)
! calculate (1 - |V|²) the square root of it
! calculate (1 - |v|²) the square root of it
!
vm = 1.0d+00 - vv
vs = sqrt(vm)
! calculate the thermal pressure and its derivative
!
! P(W) = (γ - 1)/γ (W - DΓ) (1 - |V|²)
! dP/dW = (γ - 1)/γ [(1 - D dΓ/dW) (1 - |V|²) - (W - DΓ) d|V|²/dW]
! P(W) = (γ - 1)/γ (W - DΓ) (1 - |v|²)
! dP/dW = (γ - 1)/γ [(1 - D dΓ/dW) (1 - |v|²) - (W - DΓ) d|v|²/dW]
!
pr = gammaxi * (w * vm - dn * vs)
dpw = gammaxi * (1.0d+00 + (w - dn / vs) * vv / w)
@ -3658,7 +3658,7 @@ module equations
end if
end if
! calculate |V|² from W
! calculate |v|² from W
!
vv = mm / (w * w)
@ -3710,17 +3710,24 @@ module equations
! subroutine NR_ITERATE_SRHD_ADI_2DWV:
! -----------------------------------
!
! Subroutine finds a root W of equation
! Subroutine finds a root (W,v²) of 2D equations
!
! F(W) = W - P - E = 0
! F(W,v²) = W - E - P(W,v²) = 0
! G(W,v²) = W² v² - m² = 0
!
! using the Newton-Raphson 2D iterative method.
!
! All evaluated equations incorporate already the pressure of the form
!
! P(W,|v|²) = (γ - 1)/γ (W - Γ D) (1 - |v|²)
!
! in order to optimize calculations.
!
! Arguments:
!
! mm, en - input coefficients for |M|² and E, respectively;
! bb, bm - input coefficients for |B|² and B.M, respectively;
! w, vv - input/output coefficients W and |V|²;
! w, vv - input/output coefficients W and |v|²;
!
! References:
!
@ -3799,15 +3806,12 @@ module equations
it = nmax
cn = next
! iterate using the Newton-Raphson method in order to find the roots W and |V|²
! iterate using the Newton-Raphson method in order to find the roots W and |v|²
! of functions
!
! F(W,|V|²) = W - P - E = 0
! G(W,|V|²) = |V|² W² - |M|² = 0
!
do while(keep)
! calculate W², (1 - |V|²), and the Lorentz factor
! calculate W², (1 - |v|²), and the Lorentz factor
!
ww = w * w
vm = 1.0d+00 - vv
@ -3815,27 +3819,26 @@ module equations
! calculate the thermal pressure
!
! P(W,|V|²) = (γ - 1)/γ (W - D Γ) (1 - |V|²)
!
pr = gammaxi * (w * vm - dn * vs)
! calculate F(W,|V|²) and G(W,|V|²)
! calculate F(W,|v|²) and G(W,|v|²)
!
f = w - en - pr
g = vv * ww - mm
! calculate dF(W,|V|²)/dW and dF(W,|V|²)/d|V|²
! calculate dF(W,|v|²)/dW and dF(W,|v|²)/d|v|²
!
dfw = 1.0d+00 - gammaxi * vm
dfv = 0.5d+00 * (pr / vm + gammaxi * w)
! calculate dG(W,|V|²)/dW and dG(W,|V|²)/d|V|²
! calculate dG(W,|v|²)/dW and dG(W,|v|²)/d|v|²
!
dgw = 2.0d+00 * vv * w
dgv = ww
! invert the Jacobian J = | dF/dW, dF/d|V|² |
! | dG/dW, dG/d|V|² |
! invert the Jacobian J = | dF/dW, dF/d|v|² |
! | dG/dW, dG/d|v|² |
!
det = dfw * dgv - dfv * dgw
@ -3844,12 +3847,12 @@ module equations
jfv = - dgw / det
jgv = dfw / det
! calculate increments dW and d|V|²
! calculate increments dW and d|v|²
!
dw = f * jfw + g * jgw
dv = f * jfv + g * jgv
! correct W and |V|²
! correct W and |v|²
!
w = w - dw
vv = vv - dv
@ -3911,7 +3914,7 @@ module equations
!
! All evaluated equations incorporate already the pressure of the form
!
! P(W,|V|²) = (γ - 1)/γ (W - Γ D) / (1 + |u|²)
! P(W,|u|²) = (γ - 1)/γ (W - Γ D) / (1 + |u|²)
!
! in order to optimize calculations.
!
@ -3919,7 +3922,7 @@ module equations
!
! mm, en - input coefficients for |M|² and E, respectively;
! bb, bm - input coefficients for |B|² and B.M, respectively;
! w, vv - input/output coefficients W and |V|²;
! w, vv - input/output coefficients W and |v|²;
!
!===============================================================================
!
@ -3990,7 +3993,7 @@ module equations
it = nmax
cn = next
! iterate using the Newton-Raphson method in order to find the roots W and |V|²
! iterate using the Newton-Raphson method in order to find the roots W and |u|²
! of functions
!
do while(keep)
@ -4003,7 +4006,7 @@ module equations
gm = sqrt(up)
gd = gammaxi * dn
! calculate F(W,|V|²) and G(W,|V|²)
! calculate F(W,|u|²) and G(W,|u|²)
!
f = (up - gammaxi) * w - up * en + gm * gd
g = uu * ww - up * mm
@ -4033,7 +4036,7 @@ module equations
dw = f * jfw + g * jgw
du = f * jfu + g * jgu
! correct W and |V|²
! correct W and |u|²
!
w = w - dw
uu = uu - du
@ -4059,7 +4062,7 @@ module equations
end do ! continue interations
! calculate v² from u²
! calculate |v|² from |u|²
!
vv = uu / (1.0d+00 + uu)