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EQUATIONS: Optimize SRHD 2D(W,u²) variable solver even more.

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This optimizations incorporate pressure directly into the F(W,u²)
function, while allows to reduce a few operations more.

Signed-off-by: Grzegorz Kowal <grzegorz@amuncode.org>
This commit is contained in:
Grzegorz Kowal 2015-02-20 09:28:31 -02:00
parent a9c56ff1b1
commit 1b37e6dc47
1 changed files with 12 additions and 11 deletions
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23
src/equations.F90
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@ -3909,6 +3909,12 @@ module equations
!
! 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 + |u|²)
!
! in order to optimize calculations.
!
! Arguments:
!
! mm, en - input coefficients for |M|² and E, respectively;
@ -3933,7 +3939,7 @@ module equations
logical :: keep
integer :: it, cn
real(kind=8) :: wl, wu, fl, fu
real(kind=8) :: ww, uu, up, gm, dm, pr
real(kind=8) :: ww, uu, up, gm, gd
real(kind=8) :: f, dfw, dfu, df
real(kind=8) :: g, dgw, dgu, dg
real(kind=8) :: det, jfw, jfu, jgw, jgu
@ -3989,28 +3995,23 @@ module equations
!
do while(keep)
! calculate W², (1 + |u|²), and the Lorentz factor
! calculate W², (1 + |u|²), and the Lorentz factor, and some repeated
! expressions
!
ww = w * w
up = 1.0d+00 + uu
gm = sqrt(up)
dm = gm * dn
! calculate the thermal pressure
!
! P(W,|V|²) = (γ - 1)/γ (W - D Γ) / (1 + |u|²)
!
pr = gammaxi * (w - dm) / up
gd = gammaxi * dn
! calculate F(W,|V|²) and G(W,|V|²)
!
f = (w - en - pr) * up
f = (up - gammaxi) * w - up * en + gm * gd
g = uu * ww - up * mm
! calculate dF(W,|u|²)/dW and dF(W,|u|²)/d|u|²
!
dfw = up - gammaxi
dfu = w - en - pr + gammaxi * (w - 0.5d+00 * dm) / up
dfu = w - en + 0.5d+00 * gd / gm
! calculate dG(W,|u|²)/dW and dG(W,|u|²)/d|u|²
!