diff options
Diffstat (limited to 'm/McLachlan_BSSN.m')
| -rw-r--r-- | m/McLachlan_BSSN.m | 37 |
1 files changed, 19 insertions, 18 deletions
diff --git a/m/McLachlan_BSSN.m b/m/McLachlan_BSSN.m index 30cda03..6943a3e 100644 --- a/m/McLachlan_BSSN.m +++ b/m/McLachlan_BSSN.m @@ -159,8 +159,6 @@ T11=eTxx; T12=eTxy; T22=eTyy; T13=eTxz; T23=eTyz; T33=eTzz; (* Expressions *) (******************************************************************************) -pi = N[Pi,40]; - detgExpr = Det [MatrixOfComponents [g [la,lb]]]; ddetgExpr[la_] = Sum [D[Det[MatrixOfComponents[g[la, lb]]], X] PD[X, la], @@ -171,7 +169,7 @@ ddetgtExpr[la_] = Sum [D[Det[MatrixOfComponents[gt[la, lb]]], X] PD[X, la], {X, Union[Flatten[MatrixOfComponents[gt[la, lb]]]]}]; -etaExpr = Min [SpatialBetaDriverRadius / r, 1]; +etaExpr = SpatialBetaDriverRadius / Max [r, SpatialBetaDriverRadius]; thetaExpr = Min [Exp [1 - r / SpatialShiftGammaCoeffRadius], 1]; @@ -180,8 +178,6 @@ thetaExpr = Min [Exp [1 - r / SpatialShiftGammaCoeffRadius], 1]; (* Groups *) (******************************************************************************) -SetGroupTimelevels[g_,tl_] = Join[g, {Timelevels -> tl}]; - evolvedGroups = {SetGroupName [CreateGroupFromTensor [phi ], prefix <> "log_confac"], SetGroupName [CreateGroupFromTensor [gt[la,lb]], prefix <> "metric" ], @@ -642,7 +638,7 @@ evolCalc = + 2 gtu[ui,uj] (alpha PD[Tet,lj] - Tet PD[alpha,lj]) - 2 alpha e4phi dampk1 Zet[ui] (* Equation (4.28) in Baumgarte & Shapiro (Phys. Rept. 376 (2003) 41-131) *) - + addMatter (- 16 pi alpha gtu[ui,uj] S[lj]), + + addMatter (- 16 Pi alpha gtu[ui,uj] S[lj]), dot[Xt[ui]] -> dotXt[ui], (* Equation for Theta *) @@ -665,7 +661,7 @@ evolCalc = + 2 dotTet + 2 PD[alpha,la] Zet[ua] + dampk1 alpha Tet - dampk1k2 alpha Tet (* Equation (4.21) in Baumgarte & Shapiro (Phys. Rept. 376 (2003) 41-131) *) - + addMatter (4 pi alpha (rho + trS)), + + addMatter (4 Pi alpha (rho + trS)), dot[trK] -> dottrK, (* PRD 62, 044034 (2000), eqn. (12) *) @@ -683,7 +679,7 @@ evolCalc = (* damping term in trA, alternative to trA cleaning *) (* - (dampA/3) alpha At[lc,ld] gtu[uc,ud] gt[la,lb] *) (* Equation (4.23) in Baumgarte & Shapiro (Phys. Rept. 376 (2003) 41-131) *) - + addMatter (- em4phi alpha 8 pi + + addMatter (- em4phi alpha 8 Pi (T[la,lb] - (1/3) g[la,lb] trS)), (* dot[alpha] -> - harmonicF alpha^harmonicN trK, *) @@ -700,10 +696,9 @@ evolCalc = *) dot[alpha] -> - harmonicF alpha^harmonicN (+ LapseACoeff A - + (1 - LapseACoeff) (trK - 2 Tet)), + + (1 - LapseACoeff) (trK + AlphaDriver (alpha - 1) - 2 Tet)), dot[A] -> + LapseACoeff (dottrK - 2 dotTet - AlphaDriver A), - eta -> etaExpr, theta -> thetaExpr, @@ -756,16 +751,22 @@ advectCalc = dot[At[la,lb]] -> dot[At[la,lb]] + Upwind[beta[uc], At[la,lb], lc], - dot[alpha] -> dot[alpha] + LapseAdvectionCoeff Upwind[beta[ua], alpha, la], + dot[alpha] -> dot[alpha] + + LapseAdvectionCoeff Upwind[beta[ua], alpha, la], - dot[A] -> dot[A] + LapseAdvectionCoeff Upwind[beta[ua], A, la], + dot[A] -> dot[A] + + LapseACoeff ( + + LapseAdvectionCoeff Upwind[beta[ua], A, la] + + (1 - LapseAdvectionCoeff) Upwind[beta[ua], trK, la]), - dot[beta[ua]] -> dot[beta[ua]] + ShiftAdvectionCoeff Upwind[beta[ub], beta[ua], lb], + dot[beta[ua]] -> dot[beta[ua]] + + ShiftAdvectionCoeff Upwind[beta[ub], beta[ua], lb], dot[B[ua]] -> dot[B[ua]] - + ShiftBCoeff Upwind[beta[uj], Xt[ua], lj] (* take care *) - + ShiftAdvectionCoeff Upwind[beta[ub], B[ua], lb] - - ShiftAdvectionCoeff Upwind[beta[ub], Xt[ua], lb] + + ShiftBCoeff ( + + ShiftAdvectionCoeff Upwind[beta[ub], B[ua], lb] + + ((1 - ShiftAdvectionCoeff) + Upwind[beta[ub], Xt[ua], lb])) } }; @@ -1082,7 +1083,7 @@ constraintsCalc = (* H -> trR - Km[ua,lb] Km[ub,la] + trK^2, *) (* PRD 67, 084023 (2003), eqn. (19) *) - H -> trR - Atm[ua,lb] Atm[ub,la] + (2/3) trK^2 - addMatter 16 pi rho, + H -> trR - Atm[ua,lb] Atm[ub,la] + (2/3) trK^2 - addMatter 16 Pi rho, (* gK[la,lb,lc] -> CD[K[la,lb],lc], *) (* gK[la,lb,lc] -> + 4 e4phi PD[phi,lc] At[la,lb] + e4phi CD[At[la,lb],lc] @@ -1092,7 +1093,7 @@ constraintsCalc = M[li] -> + gtu[uj,uk] (CDt[At[li,lj],lk] + 6 At[li,lj] cdphi[lk]) - (2/3) PD[trK,li] - - addMatter 8 pi S[li], + - addMatter 8 Pi S[li], (* TODO: use PRD 67, 084023 (2003), eqn. (20) *) (* det gamma-tilde *) |