EQUATIONS: Rewrite a bit esystem_roe_mhd_iso().
Signed-off-by: Grzegorz Kowal <grzegorz@amuncode.org>
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@ -2717,12 +2717,11 @@ module equations
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real(kind=8), dimension(8,8), save :: lvec, rvec
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real(kind=8), dimension(8,8), save :: lvec, rvec
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!$omp threadprivate(first, lvec, rvec)
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!$omp threadprivate(first, lvec, rvec)
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real(kind=8) :: di, btsq, bt_starsq, casq, twid_csq
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real(kind=8) :: ca, ca2, ct2, cf, cf2, cs, cs2, cf2_cs2
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real(kind=8) :: ct2, tsum, tdif, cf2_cs2, cfsq, cf, cssq, cs, ca
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real(kind=8) :: br, br2, brs, br2s, tsum, tdif, twid_c2, twid_c
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real(kind=8) :: bt, bt_star, bet2, bet3, bet2_star, bet3_star, bet_starsq
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real(kind=8) :: bty, btz, btys, btzs, bt2s, alf, als, norm
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real(kind=8) :: alpha_f, alpha_s
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real(kind=8) :: sqrtd, sgn, qf, qs, af_prime, as_prime
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real(kind=8) :: sqrtd, s, twid_c, qf, qs, af_prime, as_prime
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real(kind=8) :: cff, css, af, as, afpb, aspb, q2s, q3s, vqstr
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real(kind=8) :: norm, cff, css, af, as, afpb, aspb, q2_star, q3_star, vqstr
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!-------------------------------------------------------------------------------
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!-------------------------------------------------------------------------------
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!
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!
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@ -2733,22 +2732,22 @@ module equations
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first = .false.
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first = .false.
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end if
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end if
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! coefficients
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! coefficients for eigenvalues
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!
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!
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di = 1.0d+00 / q(idn)
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ca2 = q(ibx) * q(ibx) / q(idn)
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casq = q(ibx) * q(ibx) * di
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ca = sqrt(ca2)
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ca = sqrt(casq)
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br2 = sum(q(iby:ibz)**2)
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btsq = q(iby) * q(iby) + q(ibz) * q(ibz)
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br2s = br2 * y
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bt_starsq = btsq * y
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ct2 = br2s / q(idn)
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twid_csq = csnd2 + x
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ct2 = bt_starsq * di
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twid_c2 = csnd2 + x
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tsum = casq + ct2 + twid_csq
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tsum = ca2 + ct2 + twid_c2
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tdif = casq + ct2 - twid_csq
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tdif = ca2 + ct2 - twid_c2
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cf2_cs2 = sqrt(tdif * tdif + 4.0d+00 * twid_csq * ct2)
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cf2_cs2 = sqrt(tdif * tdif + 4.0d+00 * twid_c2 * ct2)
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cfsq = 0.5d+00 * (tsum + cf2_cs2)
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cf2 = 0.5d+00 * (tsum + cf2_cs2)
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cf = sqrt(cfsq)
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cf = sqrt(cf2)
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cssq = twid_csq * casq / cfsq
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cs2 = twid_c2 * ca2 / cf2
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cs = sqrt(cssq)
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cs = sqrt(cs2)
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! eigenvalues
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! eigenvalues
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!
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!
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@ -2767,134 +2766,134 @@ module equations
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! remaining coefficients
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! remaining coefficients
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!
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!
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bt = sqrt(btsq)
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br = sqrt(br2)
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bt_star = sqrt(bt_starsq)
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brs = sqrt(br2s)
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if (abs(bt) > 0.0d+00) then
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if (abs(br) > 0.0d+00) then
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bet2 = q(iby) / bt
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bty = q(iby) / br
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bet3 = q(ibz) / bt
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btz = q(ibz) / br
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else
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else
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bet2 = 1.0d+00
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bty = 1.0d+00
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bet3 = 0.0d+00
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btz = 0.0d+00
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end if
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end if
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bet2_star = bet2 / sqrt(y)
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btys = bty / sqrt(y)
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bet3_star = bet3 / sqrt(y)
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btzs = btz / sqrt(y)
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bet_starsq = bet2_star * bet2_star + bet3_star * bet3_star
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bt2s = btys * btys + btzs * btzs
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if (.not. abs(cfsq - cssq) > 0.0d+00) then
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if (.not. abs(cf2 - cs2) > 0.0d+00) then
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alpha_f = 1.0d+00
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alf = 1.0d+00
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alpha_s = 0.0d+00
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als = 0.0d+00
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else if ((twid_csq - cssq) <= 0.0d+00) then
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else if ((twid_c2 - cs2) <= 0.0d+00) then
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alpha_f = 0.0d+00
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alf = 0.0d+00
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alpha_s = 1.0d+00
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als = 1.0d+00
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else if ((cfsq - twid_csq) <= 0.0d+00) then
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else if ((cf2 - twid_c2) <= 0.0d+00) then
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alpha_f = 1.0d+00
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alf = 1.0d+00
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alpha_s = 0.0d+00
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als = 0.0d+00
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else
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else
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alpha_f = sqrt((twid_csq - cssq) / (cfsq - cssq))
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alf = sqrt((twid_c2 - cs2) / (cf2 - cs2))
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alpha_s = sqrt((cfsq - twid_csq) / (cfsq - cssq))
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als = sqrt((cf2 - twid_c2) / (cf2 - cs2))
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end if
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end if
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sqrtd = sqrt(q(idn))
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sqrtd = sqrt(q(idn))
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s = sign(1.0d+00, q(ibx))
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sgn = sign(1.0d+00, q(ibx))
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twid_c = sqrt(twid_csq)
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twid_c = sqrt(twid_c2)
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qf = cf * alpha_f * s
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qf = cf * alf * sgn
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qs = cs * alpha_s * s
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qs = cs * als * sgn
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af_prime = twid_c * alpha_f / sqrtd
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af_prime = twid_c * alf / sqrtd
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as_prime = twid_c * alpha_s / sqrtd
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as_prime = twid_c * als / sqrtd
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! update the varying elements of the matrix of right eigenvectors
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! === update the varying elements of the right eigenvectors matrix
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!
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!
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! left-going fast wave
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! left-going fast wave
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!
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!
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rvec(1,idn) = alpha_f
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rvec(1,idn) = alf
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rvec(1,ivx) = alpha_f * c(1)
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rvec(1,ivx) = alf * c(1)
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rvec(1,ivy) = alpha_f * q(ivy) + qs * bet2_star
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rvec(1,ivy) = alf * q(ivy) + qs * btys
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rvec(1,ivz) = alpha_f * q(ivz) + qs * bet3_star
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rvec(1,ivz) = alf * q(ivz) + qs * btzs
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rvec(1,iby) = as_prime * bet2_star
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rvec(1,iby) = as_prime * btys
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rvec(1,ibz) = as_prime * bet3_star
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rvec(1,ibz) = as_prime * btzs
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! left-going Alfvèn wave
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! left-going Alfvèn wave
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!
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!
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rvec(2,ivy) = - bet3
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rvec(2,ivy) = - btz
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rvec(2,ivz) = bet2
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rvec(2,ivz) = bty
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rvec(2,iby) = - bet3 * s / sqrtd
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rvec(2,iby) = - btz * sgn / sqrtd
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rvec(2,ibz) = bet2 * s / sqrtd
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rvec(2,ibz) = bty * sgn / sqrtd
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! left-going slow wave
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! left-going slow wave
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!
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!
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rvec(3,idn) = alpha_s
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rvec(3,idn) = als
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rvec(3,ivx) = alpha_s * c(3)
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rvec(3,ivx) = als * c(3)
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rvec(3,ivy) = alpha_s * q(ivy) - qf * bet2_star
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rvec(3,ivy) = als * q(ivy) - qf * btys
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rvec(3,ivz) = alpha_s * q(ivz) - qf * bet3_star
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rvec(3,ivz) = als * q(ivz) - qf * btzs
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rvec(3,iby) = - af_prime * bet2_star
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rvec(3,iby) = - af_prime * btys
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rvec(3,ibz) = - af_prime * bet3_star
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rvec(3,ibz) = - af_prime * btzs
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! right-going slow wave
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! right-going slow wave
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!
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!
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rvec(5,idn) = alpha_s
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rvec(5,idn) = als
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rvec(5,ivx) = alpha_s * c(5)
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rvec(5,ivx) = als * c(5)
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rvec(5,ivy) = alpha_s * q(ivy) + qf * bet2_star
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rvec(5,ivy) = als * q(ivy) + qf * btys
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rvec(5,ivz) = alpha_s * q(ivz) + qf * bet3_star
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rvec(5,ivz) = als * q(ivz) + qf * btzs
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rvec(5,iby) = rvec(3,iby)
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rvec(5,iby) = rvec(3,iby)
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rvec(5,ibz) = rvec(3,ibz)
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rvec(5,ibz) = rvec(3,ibz)
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! right-going Alfvèn wave
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! right-going Alfvèn wave
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!
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!
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rvec(6,ivy) = bet3
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rvec(6,ivy) = btz
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rvec(6,ivz) = - bet2
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rvec(6,ivz) = - bty
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rvec(6,iby) = rvec(2,iby)
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rvec(6,iby) = rvec(2,iby)
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rvec(6,ibz) = rvec(2,ibz)
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rvec(6,ibz) = rvec(2,ibz)
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! right-going fast wave
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! right-going fast wave
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!
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!
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rvec(7,idn) = alpha_f
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rvec(7,idn) = alf
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rvec(7,ivx) = alpha_f * c(7)
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rvec(7,ivx) = alf * c(7)
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rvec(7,ivy) = alpha_f * q(ivy) - qs * bet2_star
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rvec(7,ivy) = alf * q(ivy) - qs * btys
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rvec(7,ivz) = alpha_f * q(ivz) - qs * bet3_star
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rvec(7,ivz) = alf * q(ivz) - qs * btzs
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rvec(7,iby) = rvec(1,iby)
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rvec(7,iby) = rvec(1,iby)
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rvec(7,ibz) = rvec(1,ibz)
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rvec(7,ibz) = rvec(1,ibz)
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! update the varying elements of the matrix of left eigenvectors
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! === update the varying elements of the left eigenvectors matrix
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!
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!
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norm = 0.5d+00 / twid_csq
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norm = 2.0d+00 * twid_c2
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cff = norm * alpha_f * cf
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cff = alf * cf / norm
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css = norm * alpha_s * cs
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css = als * cs / norm
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qf = qf * norm
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qf = qf / norm
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qs = qs * norm
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qs = qs / norm
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af = norm * af_prime * q(idn)
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af = af_prime * q(idn) / norm
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as = norm * as_prime * q(idn)
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as = as_prime * q(idn) / norm
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afpb = norm * af_prime * bt_star
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afpb = af_prime * brs / norm
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aspb = norm * as_prime * bt_star
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aspb = as_prime * brs / norm
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q2_star = bet2_star / bet_starsq
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q2s = btys / bt2s
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q3_star = bet3_star / bet_starsq
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q3s = btzs / bt2s
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vqstr = q(ivy) * q2_star + q(ivz) * q3_star
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vqstr = q(ivy) * q2s + q(ivz) * q3s
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! left-going fast wave
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! left-going fast wave
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!
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!
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lvec(idn,1) = cff * c(7) - qs * vqstr - aspb
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lvec(idn,1) = cff * c(7) - qs * vqstr - aspb
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lvec(ivx,1) = - cff
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lvec(ivx,1) = - cff
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lvec(ivy,1) = qs * q2_star
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lvec(ivy,1) = qs * q2s
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lvec(ivz,1) = qs * q3_star
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lvec(ivz,1) = qs * q3s
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lvec(iby,1) = as * q2_star
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lvec(iby,1) = as * q2s
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lvec(ibz,1) = as * q3_star
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lvec(ibz,1) = as * q3s
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! left-going Alfvèn wave
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! left-going Alfvèn wave
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!
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!
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lvec(idn,2) = 0.5d+00 * (q(ivy) * bet3 - q(ivz) * bet2)
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lvec(idn,2) = 0.5d+00 * (q(ivy) * btz - q(ivz) * bty)
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lvec(ivy,2) = - 0.5d+00 * bet3
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lvec(ivy,2) = - 0.5d+00 * btz
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lvec(ivz,2) = 0.5d+00 * bet2
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lvec(ivz,2) = 0.5d+00 * bty
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lvec(iby,2) = - 0.5d+00 * sqrtd * bet3 * s
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lvec(iby,2) = - 0.5d+00 * sqrtd * btz * sgn
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lvec(ibz,2) = 0.5d+00 * sqrtd * bet2 * s
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lvec(ibz,2) = 0.5d+00 * sqrtd * bty * sgn
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! left-going slow wave
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! left-going slow wave
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!
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!
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lvec(idn,3) = css * c(5) + qf * vqstr + afpb
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lvec(idn,3) = css * c(5) + qf * vqstr + afpb
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lvec(ivx,3) = - css
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lvec(ivx,3) = - css
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lvec(ivy,3) = - qf * q2_star
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lvec(ivy,3) = - qf * q2s
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lvec(ivz,3) = - qf * q3_star
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lvec(ivz,3) = - qf * q3s
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lvec(iby,3) = - af * q2_star
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lvec(iby,3) = - af * q2s
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lvec(ibz,3) = - af * q3_star
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lvec(ibz,3) = - af * q3s
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! right-going slow wave
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! right-going slow wave
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!
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!
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