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# This is an until-end-of-line comment
THORN BSSN
DERIVATIVE
PDstandardNth[i_] -> StandardCenteredDifferenceOperator[1,derivOrder/2,i]
DERIVATIVE
PDstandardNth[i_,i_] -> StandardCenteredDifferenceOperator[2,derivOrder/2,i]
DERIVATIVE
PDstandardNth[i_,j_] -> StandardCenteredDifferenceOperator[1,derivOrder/2,i] *
StandardCenteredDifferenceOperator[1,derivOrder/2,j]
DERIVATIVE
PDdissipationNth[i_] ->
spacing[i]^(derivOrder+1) / 2^(derivOrder+2) *
StandardCenteredDifferenceOperator[derivOrder+2,derivOrder/2+1,i]
JACOBIAN {PD, FD, J, dJ}
TENSOR normal, tangentA, tangentB, dir
TENSOR xx, rr, th, ph
TENSOR J, dJ
TENSOR admg, admK, admalpha, admdtalpha, admbeta, admdtbeta, H, M
TENSOR g, detg, gu, G, R, trR, Km, trK, cdphi, cdphi2
TENSOR phi, gt, At, Xt, Xtn, alpha, A, beta, B, Atm, Atu, trA, Ats, trAts
TENSOR dottrK, dotXt
TENSOR cXt, cS, cA
TENSOR e4phi, em4phi, ddetg, detgt, gtu, ddetgt, dgtu, ddgtu, Gtl, Gtlu, Gt
TENSOR Rt, Rphi, gK
TENSOR T00, T0, T, rho, S
TENSOR x, y, z, r
TENSOR epsdiss
SYMMETRIC admg[la,lb], admK[la,lb]
SYMMETRIC g[la,lb], K[la,lb], R[la,lb], cdphi2[la,lb]
SYMMETRIC gt[la,lb], At[la,lb], Ats[la,lb], Rt[la,lb], Rphi[la,lb], T[la,lb]
SYMMETRIC {dJ[ua,lb,lc], lb, lc}
SYMMETRIC {G[ua,lb,lc], lb, lc}
SYMMETRIC {Gtl[la,lb,lc], lb, lc}
SYMMETRIC {Gt[ua,lb,lc], lb, lc}
SYMMETRIC {gK[la,lb,lc], la, lb}
SYMMETRIC gu[ua,ub], gtu[ua,ub], Atu[ua,ub]
SYMMETRIC {dgtu[ua,ub,lc], ua, ub}
SYMMETRIC {ddgtu[ua,ub,lc,ld], ua, ub}
SYMMETRIC {ddgtu[ua,ub,lc,ld], lc, ld}
CONNECTION {CD, PD, G}
CONNECTION {CDt, PD, Gt}
GROUP {phi , "log_confac"}
GROUP {gt[la,lb], "metric" }
GROUP {Xt[ua ], "Gamma" }
EXTRA_GROUP {"Grid::coordinates", {x, y, z, r}}
EXTRA_GROUP {"ADMBase::metric", {gxx, gxy, gxz, gyy, gyz, gzz}}
EXTRA_GROUP {"ADMBase::curv", {kxx, kxy, kxz, kyy, kyz, kzz}}
DEFINE pi = N[Pi,40]
DEFINE
detgExpr = Det [MatrixOfComponents [g [la,lb]]]
DEFINE
ddetgExpr[la_] =
Sum [D[Det[MatrixOfComponents[g[la, lb]]], X] PD[X, la],
{X, Union[Flatten[MatrixOfComponents[g[la, lb]]]]}]
DEFINE
detgtExpr = Det [MatrixOfComponents [gt[la,lb]]]
DEFINE
ddetgtExpr[la_] =
Sum [D[Det[MatrixOfComponents[gt[la, lb]]], X] PD[X, la],
{X, Union[Flatten[MatrixOfComponents[gt[la, lb]]]]}]
CALCULATION "Minkowski"
Schedule: {"IN ADMBase_InitialData"}
ConditionalOnKeyword: {"my_initial_data", "Minkowski"}
BEGIN EQUATIONS
phi -> IfThen[conformalMethod, 1, 0]
phi -> conformalMethod ? 1 : 0
gt[la,lb] -> KD[la,lb]
trK -> 0
At[la,lb] -> 0
Xt[ua] -> 0
alpha -> 1
A -> 0
beta[ua] -> 0
B[ua] -> 0
END EQUATIONS
END CALCULATION
CALCULATION "convertFromADMBase"
Schedule: {"AT initial AFTER ADMBase_PostInitial"}
ConditionalOnKeyword: {"my_initial_data", "ADMBase"}
SHORTHAND g[la,lb], detg, gu[ua,ub], em4phi
BEGIN EQUATIONS
g[la,lb] -> admg[la,lb]
detg -> detgExpr
gu[ua,ub] -> 1/detg detgExpr MatrixInverse [g[ua,ub]]
phi -> IfThen [conformalMethod, detg^(-1/6), Log[detg]/12]
em4phi -> IfThen [conformalMethod, phi^2, Exp[-4 phi]]
gt[la,lb] -> em4phi g[la,lb]
trK -> gu[ua,ub] admK[la,lb]
At[la,lb] -> em4phi (admK[la,lb] - (1/3) g[la,lb] trK)
alpha -> admalpha
beta[ua] -> admbeta[ua]
END EQUATIONS
END CALCULATION
CALCULATION convertFromADMBaseGammaCalc
Name: BSSN <> "_convertFromADMBaseGamma"
Schedule: {"AT initial AFTER " <> BSSN <> "_convertFromADMBase"}
ConditionalOnKeyword: {"my_initial_data", "ADMBase"}
# Do not synchronise right after this routine; instead, synchronise
# after extrapolating
Where: Interior
# Synchronise after this routine, so that the refinement boundaries
# are set correctly before extrapolating. (We will need to
# synchronise again after extrapolating because extrapolation does
# not fill ghost zones, but this is irrelevant here.)
SHORTHAND dir[ua]
SHORTHAND detgt, gtu[ua,ub], Gt[ua,lb,lc], theta
BEGIN EQUATIONS
dir[ua] -> Sign[beta[ua]]
detgt -> 1 (* detgtExpr *)
gtu[ua,ub] -> 1/detgt detgtExpr MatrixInverse [gt[ua,ub]]
Gt[ua,lb,lc] -> 1/2 gtu[ua,ud]
(PD[gt[lb,ld],lc] + PD[gt[lc,ld],lb] - PD[gt[lb,lc],ld])
Xt[ua] -> gtu[ub,uc] Gt[ua,lb,lc]
# If LapseACoeff=0, then A is not evolved, in the sense that it
# does not influence the time evolution of other variables.
A -> IfThen [LapseACoeff != 0
1 / (- harmonicF alpha^harmonicN)
(+ admdtalpha
- LapseAdvectionCoeff beta[ua] PDua[alpha,la]
- LapseAdvectionCoeff Abs[beta[ua]] PDus[alpha,la])
0]
theta -> thetaExpr
# If ShiftBCoeff=0 or theta ShiftGammaCoeff=0, then B^i is not
# evolved, in the sense that it does not influence the time
# evolution of other variables.
B[ua] -> IfThen [ShiftGammaCoeff ShiftBCoeff != 0
1 / (theta ShiftGammaCoeff)
(+ admdtbeta[ua]
- ShiftAdvectionCoeff beta[ub] PDua[beta[ua],lb]
- ShiftAdvectionCoeff Abs[beta[ub]] PDus[beta[ua],lb])
0]
END EQUATIONS
END CALCULATION
INHERITED_IMPLEMENTATION ADMBase, TmunuBase
KEYWORD_PARAMETER "my_initial_data"
# Visibility: "restricted"
# Description: "ddd"
AllowedValues: {"ADMBase", "Minkowski"}
Default: "ADMBase"
END KEYWORD_PARAMETER
REAL_PARAMETER LapseACoeff
Description: "Whether to evolve A in time"
Default: 0
END REAL_PARAMETER
END THORN
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