Sets metric in some coordinates based upon metric.h type choice for MCOORD this file includes metric dependent terms, including for initial condition routines for IC coords. More...

#include "decs.h"

Include dependency graph for metric.c:

Go to the source code of this file.

Macros
#define	FLATSPACE 0

#define	NOSPIN 1

#define	FULLHT 2

#define	HTMETRICTYPE FULLHT

#define	FLATSPACE 0

#define	NOSPIN 1

#define	FULLHT 2

#define	HTMETRICTYPE FULLHT

#define	ks_gcov00 (-1. + MSQ/rho2small)

#define	ks_gcov01 (MSQ/rho2small)

#define	ks_gcov02 (0)

#define	ks_gcov03 (-MSQas2/rho2small)

#define	ks_gcov10 (ks_gcov01)

#define	ks_gcov11 (1. + MSQ/rho2small)

#define	ks_gcov12 (0)

#define	ks_gcov13 (-as2(1. + MSQ/rho2small))

#define	ks_gcov20 (0)

#define	ks_gcov21 (0)

#define	ks_gcov22 (rho2)

#define	ks_gcov23 (0)

#define	ks_gcov30 (ks_gcov03)

#define	ks_gcov31 (ks_gcov13)

#define	ks_gcov32 (0)

#define	ks_gcov33 (s2(rho2 + aas2(1. + MSQ/rho2small)))

#define	bl_gcov00 (-(1. - MSQ/(r2small*mu)))

#define	bl_gcov01 (0)

#define	bl_gcov02 (0)

#define	bl_gcov03 (-MSQas2/(r2small*mu))

#define	bl_gcov10 (0)

#define	bl_gcov11 (mu/DD)

#define	bl_gcov12 (0)

#define	bl_gcov13 (0)

#define	bl_gcov20 (0)

#define	bl_gcov21 (0)

#define	bl_gcov22 (r2*mu)

#define	bl_gcov23 (0)

#define	bl_gcov30 (bl_gcov03)

#define	bl_gcov31 (0)

#define	bl_gcov32 (0)

#define	bl_gcov33 (r2sthsth(1. + a2/r2small + MSQa2s2/(r2smallr2small*mu)))

#define	ks_gcon00 (-(1.+ MSQ/rho2))

#define	ks_gcon01 (MSQ/rho2)

#define	ks_gcon02 (0)

#define	ks_gcon03 (0)

#define	ks_gcon10 (ks_gcon01)

#define	ks_gcon11 ((rr+aa-MSQ)/rho2)

#define	ks_gcon12 (0)

#define	ks_gcon13 (a/rho2)

#define	ks_gcon20 (ks_gcon02)

#define	ks_gcon21 (ks_gcon12)

#define	ks_gcon22 (1./rho2)

#define	ks_gcon23 (0)

#define	ks_gcon30 (ks_gcon03)

#define	ks_gcon31 (ks_gcon13)

#define	ks_gcon32 (ks_gcon23)

#define	ks_gcon33 (1./(rho2*s2))

#define	bl_gcon00 (-1. - MSQ(1. + a2/r2small)/(r2smallDD*mu))

#define	bl_gcon01 (0)

#define	bl_gcon02 (0)

#define	bl_gcon03 (-MSQa/(r2smallr2smallDDmu))

#define	bl_gcon10 (0)

#define	bl_gcon11 (DD/mu)

#define	bl_gcon12 (0)

#define	bl_gcon13 (0)

#define	bl_gcon20 (0)

#define	bl_gcon21 (0)

#define	bl_gcon22 (1./(r2small*mu))

#define	bl_gcon23 (0)

#define	bl_gcon30 (bl_gcon03)

#define	bl_gcon31 (0)

#define	bl_gcon32 (0)

#define	bl_gcon33 ((1. - MSQ/(r2smallmu))/(r2smallsthsthDD))

#define	M (1.)

#define	IDXR(a, R0, r, th, rl, rh) ((pow(a,2) + 2.pow(r,2) + pow(a,2)cos(2.th))/((rh - 1.rl)(2.R0 + rh + rl) + (pow(a,2) + 2.pow(R0,2))(log(-1.R0 + rh) - 1.log(-1.R0 + rl)) + pow(a,2)cos(2.th)(log(-1.R0 + rh) - 1.log(-1.*R0 + rl))))

#define	IDXTH(a, R0, r, th, thl, thh) ((-3.M_PI(pow(a,2) + 2.pow(r,2) + pow(a,2)cos(2.th))sin(th))/(cos(thh)(pow(a,2) + 6.pow(r,2) + pow(a,2)cos(2.thh)) - 1.cos(thl)(pow(a,2) + 6.pow(r,2) + pow(a,2)cos(2.*thl))))

#define	FIDXR(a, R0, r, th) ((pow(a,2) + 2.pow(r,2) + pow(a,2)cos(2.th))/(4.R0(-1.R0 + r) + pow(-1.R0 + r,2) + (pow(a,2) + 2.pow(R0,2) + pow(a,2)cos(2.th))log(-1.R0 + r)))

#define	FIDXTH(a, R0, r, th) ((-3.pow(a,2)sin(2.th) - 6.pow(r,2)tan(th))/(pow(a,2) + 6.pow(r,2) + pow(a,2)cos(2.th)))

Functions
void	gcov_func (struct of_geom ptrgeom, int getprim, int whichcoord, FTYPE X, FTYPE gcovinfunc, FTYPE gcovpertinfunc)
	obtain gcov in primcoords of whichcoord type metric/coords here ptrgeom is only expected to contain i,j,k,p location More...

int	rotate_VtoVmetric (int whichcoord, FTYPE ROTANGLE, FTYPE V, FTYPE Vmetric)
	Rotate V[X] (r,thnew,phnew as in bl_coord) to Vmetric (r,th,ph as in set_gcov) That is, when using rotated metric, we assume metric itself still has Vmetric=r,th,ph, while X is mapped to V=rnew,hnew,phnew. More...

int	rotate_VmetrictoV (int whichcoord, FTYPE ROTANGLE, FTYPE Vmetric, FTYPE V)
	perform rotation of V (for spherical polar coordinates) More...

void	gcon_func (struct of_geom ptrgeom, int getprim, int whichcoord, FTYPE X, FTYPE gcov, FTYPE gcon)
	obtain prim gcon in primcoords of whichcoord type metric/coords More...

void	conn_func (int whichcoord, FTYPE X, struct of_geom geom, FTYPE(conn)[NDIM][NDIM], FTYPE conn2)
	connection not simply transformed – so compute directly from final metric (primcoords) More...

void	set_gcov_ksmetric (FTYPE V, FTYPE gcov, FTYPE *gcovpert)
	(~t,r,,~) More...

void	set_gcon_ksmetric (FTYPE V, FTYPE gcon)
	g^{} (analytic or numerical) More...

void	set_conn_general (FTYPE X, struct of_geom geom, FTYPE(conn)[NDIM][NDIM], FTYPE conn2)
	CONNECTIONS (numerical or analytic) More...

void	set_conn_ksmetric (FTYPE X, struct of_geom geom, FTYPE(conn)[NDIM][NDIM], FTYPE conn2)

void	gdetvol_func (struct of_geom ptrgeom, FTYPE gdettrue, FTYPE EOMFUNCNAME, FTYPE gdetvol)
	geometry only contains i,j,k,p only for spherical polar coordinates with negligible relativistic effects only used if GDETVOLDIFF==1 More...

Detailed Description

Sets metric in some coordinates based upon metric.h type choice for MCOORD this file includes metric dependent terms, including for initial condition routines for IC coords.

crucially need to setup analytic form of gcov. All rest can be done numerically or analytically if wanted. SUPERNOTE: Set DOMIXTHETAPHI to 0 or 1 in definit.h!! self-gravity TODO: http://www.fftw.org/ COSMOS++ uses: https://computation.llnl.gov/casc/hypre/software.html http://ciera.northwestern.edu/StarCrash/manual/html/node3.html http://ccfd-jacob.blogspot.com http://farside.ph.utexas.edu/teaching/329/lectures/node60.html

Definition in file metric.c.

Macro Definition Documentation

#define bl_gcon00 (-1. - MSQ*(1. + a2/r2small)/(r2small*DD*mu))

#define bl_gcon01 (0)

#define bl_gcon02 (0)

#define bl_gcon03 (-MSQ*a/(r2small*r2small*DD*mu))

#define bl_gcon10 (0)

#define bl_gcon11 (DD/mu)

#define bl_gcon12 (0)

#define bl_gcon13 (0)

#define bl_gcon20 (0)

#define bl_gcon21 (0)

#define bl_gcon22 (1./(r2small*mu))

#define bl_gcon23 (0)

#define bl_gcon30 (bl_gcon03)

#define bl_gcon31 (0)

#define bl_gcon32 (0)

#define bl_gcon33 ((1. - MSQ/(r2small*mu))/(r2small*sth*sth*DD))

#define bl_gcov00 (-(1. - MSQ/(r2small*mu)))

#define bl_gcov01 (0)

#define bl_gcov02 (0)

#define bl_gcov03 (-MSQ*a*s2/(r2small*mu))

#define bl_gcov10 (0)

#define bl_gcov11 (mu/DD)

#define bl_gcov12 (0)

#define bl_gcov13 (0)

#define bl_gcov20 (0)

#define bl_gcov21 (0)

#define bl_gcov22 (r2*mu)

#define bl_gcov23 (0)

#define bl_gcov30 (bl_gcov03)

#define bl_gcov31 (0)

#define bl_gcov32 (0)

#define bl_gcov33 (r2*sth*sth*(1. + a2/r2small + MSQ*a2*s2/(r2small*r2small*mu)))

#define FIDXR	(	a,
		R0,
		r,
		th
	)	((pow(a,2) + 2.pow(r,2) + pow(a,2)cos(2.th))/(4.R0(-1.R0 + r) + pow(-1.R0 + r,2) + (pow(a,2) + 2.pow(R0,2) + pow(a,2)cos(2.th))log(-1.R0 + r)))

#define FIDXTH	(	a,
		R0,
		r,
		th
	)	((-3.pow(a,2)sin(2.th) - 6.pow(r,2)tan(th))/(pow(a,2) + 6.pow(r,2) + pow(a,2)cos(2.th)))

#define FLATSPACE 0

#define FULLHT 2

#define HTMETRICTYPE FULLHT

#define IDXR	(	a,
		R0,
		r,
		th,
		rl,
		rh
	)	((pow(a,2) + 2.pow(r,2) + pow(a,2)cos(2.th))/((rh - 1.rl)(2.R0 + rh + rl) + (pow(a,2) + 2.pow(R0,2))(log(-1.R0 + rh) - 1.log(-1.R0 + rl)) + pow(a,2)cos(2.th)(log(-1.R0 + rh) - 1.log(-1.*R0 + rl))))

#define IDXTH	(	a,
		R0,
		r,
		th,
		thl,
		thh
	)	((-3.M_PI(pow(a,2) + 2.pow(r,2) + pow(a,2)cos(2.th))sin(th))/(cos(thh)(pow(a,2) + 6.pow(r,2) + pow(a,2)cos(2.thh)) - 1.cos(thl)(pow(a,2) + 6.pow(r,2) + pow(a,2)cos(2.*thl))))

#define ks_gcon00 (-(1.+ MSQ/rho2))

#define ks_gcon01 (MSQ/rho2)

#define ks_gcon02 (0)

#define ks_gcon03 (0)

#define ks_gcon10 (ks_gcon01)

#define ks_gcon11 ((r*r+a*a-MSQ)/rho2)

#define ks_gcon12 (0)

#define ks_gcon13 (a/rho2)

#define ks_gcon20 (ks_gcon02)

#define ks_gcon21 (ks_gcon12)

#define ks_gcon22 (1./rho2)

#define ks_gcon23 (0)

#define ks_gcon30 (ks_gcon03)

#define ks_gcon31 (ks_gcon13)

#define ks_gcon32 (ks_gcon23)

#define ks_gcon33 (1./(rho2*s2))

#define ks_gcov00 (-1. + MSQ/rho2small)

#define ks_gcov01 (MSQ/rho2small)

#define ks_gcov02 (0)

#define ks_gcov03 (-MSQ*a*s2/rho2small)

#define ks_gcov10 (ks_gcov01)

#define ks_gcov11 (1. + MSQ/rho2small)

#define ks_gcov12 (0)

#define ks_gcov13 (-a*s2*(1. + MSQ/rho2small))

#define ks_gcov20 (0)

#define ks_gcov21 (0)

#define ks_gcov22 (rho2)

#define ks_gcov23 (0)

#define ks_gcov30 (ks_gcov03)

#define ks_gcov31 (ks_gcov13)

#define ks_gcov32 (0)

#define ks_gcov33 (s2*(rho2 + a*a*s2*(1. + MSQ/rho2small)))

#define M (1.)

Definition at line 2332 of file metric.c.

#define NOSPIN 1

Function Documentation

void conn_func	(	int	whichcoord,
		FTYPE *	X,
		struct of_geom *	geom,
		FTYPE(*)	conn[NDIM][NDIM],
		FTYPE *	conn2
	)

connection not simply transformed – so compute directly from final metric (primcoords)

Definition at line 744 of file metric.c.

Here is the call graph for this function:

Here is the caller graph for this function:

void gcon_func	(	struct of_geom *	ptrgeom,
		int	getprim,
		int	whichcoord,
		FTYPE *	X,
		FTYPE *	gcov,
		FTYPE *	gcon
	)

obtain prim gcon in primcoords of whichcoord type metric/coords

Definition at line 678 of file metric.c.

Here is the call graph for this function:

Here is the caller graph for this function:

void gcov_func	(	struct of_geom *	ptrgeom,
		int	getprim,
		int	whichcoord,
		FTYPE *	X,
		FTYPE *	gcovinfunc,
		FTYPE *	gcovpertinfunc
	)

obtain gcov in primcoords of whichcoord type metric/coords here ptrgeom is only expected to contain i,j,k,p location

Definition at line 24 of file metric.c.

Here is the caller graph for this function:

void gdetvol_func	(	struct of_geom *	ptrgeom,
		FTYPE *	gdettrue,
		FTYPE *	EOMFUNCNAME,
		FTYPE *	gdetvol
	)

geometry only contains i,j,k,p only for spherical polar coordinates with negligible relativistic effects only used if GDETVOLDIFF==1

Definition at line 3631 of file metric.c.

Here is the call graph for this function:

Here is the caller graph for this function:

int rotate_VmetrictoV	(	int	whichcoord,
		FTYPE	ROTANGLE,
		FTYPE *	Vmetric,
		FTYPE *	V
	)

perform rotation of V (for spherical polar coordinates)

This takes input of V=(t,r,h,ph) and gives back Vmetric=(t,r,hnew,phnew) where h,ph are in original metric form and hnew,phnew are rotated versions

So since we want X->V to be mapping V=(t,r,hnew,phnew), this is not to be used.

This can be used in (e.g.) init.py to have python script take data (in Vnew=V) and obtain Vmetric version

1) transVtoVmetric(gcovnew) gives gcov[original metric] 2) transVtoVmetric(ucon,bcon,ucov,bcov) or transVmetrictoV(ucon,bcon,ucov,bcov) 3) Rotate actual spatial positions of data, including metrics, so that again axisymmetric so only have to store 1 phi slice!

Definition at line 485 of file metric.c.

int rotate_VtoVmetric	(	int	whichcoord,
		FTYPE	ROTANGLE,
		FTYPE *	V,
		FTYPE *	Vmetric
	)

Rotate V[X] (r,thnew,phnew as in bl_coord) to Vmetric (r,th,ph as in set_gcov) That is, when using rotated metric, we assume metric itself still has Vmetric=r,th,ph, while X is mapped to V=rnew,hnew,phnew.

So input to set_gcov(X,V) needs to then get V->Vmetric before getting gcov(Vmetric). So real spherical polar coordinates for grid itself is V=rnew,hnew,phnew.

Use this rather than direct transformation(rnew,hnew,phnew) because that expression becomes too complicated in mathematica. So just take 3 steps: 1) gcov_func(X,V) 2) rotate_VtoVmetric(V,Vmetric) 3) set_gcov...(Vmetric) 4) transVmetrictoV(gcov) (which internally uses rotate_VtoVmetric() to keep expressions simple (i.e. kept in terms of Vmetric)

#2 just accounts for Vmetric[V[X]] as far as assignment of metric values so that X[] grid has used correct values of old/metric r,h,ph #4 accounts for differentials in metric so that ds^2 is the same. This is written in terms of V=rnew,hnew,phnew, so can just feed-in V[X].

Definition at line 378 of file metric.c.

Here is the caller graph for this function: