diff options
| author | Bernard Kelly <bernard.j.kelly@nasa.gov> | 2013-04-15 09:25:41 +0200 |
|---|---|---|
| committer | Ian Hinder <ian.hinder@aei.mpg.de> | 2013-04-15 15:53:41 +0200 |
| commit | 976593d219b2e0785540b1168cd58cffb0e3c76d (patch) | |
| tree | 9f20f51b687963d7c2c3fdcdba50e357c1adb28b | |
| parent | d382b047ef15f6bcf81f75deb5f87e6c62c1e2d0 (diff) | |
McLachlan_BSSN.m: Correct harmonic shift for conformalMethod = phi
The harmonic shift equations implemented in
7f81c9901489f8a94493320a27437bd125b69010 are correct only for the W
conformal method, and lead to wrong results if the phi conformal
method is used. This commit corrects this.
| -rw-r--r-- | m/McLachlan_BSSN.m | 37 |
1 files changed, 22 insertions, 15 deletions
diff --git a/m/McLachlan_BSSN.m b/m/McLachlan_BSSN.m index 333b478..484bae7 100644 --- a/m/McLachlan_BSSN.m +++ b/m/McLachlan_BSSN.m @@ -109,7 +109,7 @@ Map [DefineTensor, alpha, A, beta, B, Atm, Atu, trA, Ats, trAts, dottrK, dotXt, cXt, cS, cA, - e4phi, em4phi, ddetg, detgt, gtu, ddetgt, dgtu, ddgtu, Gtl, Gtlu, Gt, + e4phi, em4phi, ddetg, detgt, gtu, ddetgt, dgtu, ddgtu, Gtl, Gtlu, Gt, Ddetgt, Rt, Rphi, gK, T00, T0, T, rho, S, x, y, z, r, @@ -407,7 +407,7 @@ convertToADMBaseDtLapseShiftCalc = Schedule -> {"IN " <> thorn <> "_convertToADMBaseGroup"}, ConditionalOnKeyword -> {"dt_lapse_shift_method", "correct"}, Where -> Interior, - Shorthands -> {dir[ua], detgt, gtu[ua,ub], eta, theta}, + Shorthands -> {dir[ua], detgt, gtu[ua,ub], eta, theta, em4phi, Ddetgt[la]}, Equations -> { dir[ua] -> Sign[beta[ua]], @@ -415,10 +415,15 @@ convertToADMBaseDtLapseShiftCalc = detgt -> 1 (* detgtExpr *), (* This leads to simpler code... *) gtu[ua,ub] -> 1/detgt detgtExpr MatrixInverse [gt[ua,ub]], + em4phi -> IfThen[conformalMethod==CMW, phi^2, Exp[-4 phi]], eta -> etaExpr, theta -> thetaExpr, - + + (* Ddetgt should be zero analytically, but we're not assuming it here. Change commenting to assume it.*) + Ddetgt[la] -> gtu[uk,ul] PD[gt[lk,ll],la], + (*Ddetgt[la] -> 0,*) + (* see RHS *) (* admdtalpha -> - harmonicF alpha^harmonicN @@ -431,11 +436,10 @@ convertToADMBaseDtLapseShiftCalc = (trK - IfCCZ4[2 Theta, 0]))) + LapseAdvectionCoeff Upwind[beta[ua], alpha, la], admdtbeta[ua] -> IfThen[harmonicShift, - - 1/2 gtu[ua,uj] phi alpha - (- 2 alpha PD[phi,lj] - + 2 phi PD[alpha,lj] - + gtu[uk,ul] phi alpha - (PD[gt[lk,ll],lj] - 2 PD[gt[lj,lk],ll])), + - 1/2 gtu[ua,uj] em4phi alpha + (- 2 alpha IfThen[conformalMethod==CMW,1/phi,-2] PD[phi,lj] + + 2 PD[alpha,lj] + + alpha (Ddetgt[lj] - 2 gtu[uk,ul] PD[gt[lj,lk],ll])), (* else *) + theta ShiftGammaCoeff (+ ShiftBCoeff B[ua] @@ -540,7 +544,7 @@ evolCalc = e4phi, em4phi, cdphi[la], cdphi2[la,lb], g[la,lb], detg, gu[ua,ub], Ats[la,lb], trAts, eta, theta, rho, S[la], trS, fac1, fac2, dottrK, dotXt[ua], - epsdiss[ua], IfCCZ4[Z[ua]], IfCCZ4[dotTheta]}, + epsdiss[ua], IfCCZ4[Z[ua]], IfCCZ4[dotTheta], Ddetgt[la]}, Equations -> { dir[ua] -> Sign[beta[ua]], @@ -721,15 +725,18 @@ evolCalc = eta -> etaExpr, theta -> thetaExpr, - + + (* Ddetgt should be zero analytically, but we're not assuming it here. Change commenting to assume it.*) + Ddetgt[la] -> gtu[uk,ul] PD[gt[lk,ll],la], + (*Ddetgt[la] -> 0,*) + (* dot[beta[ua]] -> eta Xt[ua], *) (* dot[beta[ua]] -> ShiftGammaCoeff alpha^ShiftAlphaPower B[ua], *) dot[beta[ua]] -> IfThen[harmonicShift, - - 1/2 gtu[ua,uj] phi alpha - (- 2 alpha PD[phi,lj] - + 2 phi PD[alpha,lj] - + gtu[uk,ul] phi alpha - (PD[gt[lk,ll],lj] - 2 PD[gt[lj,lk],ll])), + - 1/2 gtu[ua,uj] em4phi alpha + (- 2 alpha IfThen[conformalMethod==CMW,1/phi,-2] PD[phi,lj] + + 2 PD[alpha,lj] + + alpha (Ddetgt[lj] - 2 gtu[uk,ul] PD[gt[lj,lk],ll])), (* else *) + theta ShiftGammaCoeff (+ ShiftBCoeff B[ua] |