precondMatrices.f90 File Reference

Collection of matrices and operators for low Mach-number preconditioning. All formulations assume general 3-D flow. More...

Functions/Subroutines
real(rtype) function	comptheta (gam, c, q2)
	Computes the preconditioning parameter theta. More...
subroutine	prim2cons (wvec, wpvec, H, theta, rhoT, hp, hT, pmat)
	Computes transformation matrix from primitive to conservative variables P (equivalent to the preconditioning matrix G). More...
subroutine	cons2prim (wvec, wpvec, H, q2, theta, rhoT, hp, hT, pmat1)
	Computes transformation matrix from conservative to primitive variables P^-1 (equivalent to the inverse of the preconditioning matrix G^-1). More...
subroutine	lefteigenvec (wvec, wpvec, nvec, V, theta, rhop, rhoT, hp, hT, evl)
	Computes matrix of left eigenvectors of G^-1*A_c,p (i.e., (T_p)^-1). More...
subroutine	righteigenvec (wvec, wpvec, nvec, V, H, theta, rhop, rhoT, hp, hT, evr)
	Computes matrix of right eigenvectors of G^-1*A_c,p multiplied by the preconditioning matrix G (i.e., G*T_p). More...
subroutine	matprodtp1_p1 (wvec, wpvec, nvec, V, H, theta, rhop, rhoT, hp, hT, q2, mat)
	Computes matrix product (T_p^-1) * (P^-1). More...
subroutine	matrixtimesinverse (wpvec, q2, amat, bmat, cmat)
	Computes matrix times the inverse of a similar matrix, where both matrices have the structure of the preconditioning (or the transformation) matrix. Thus, products like P*G^-1 or G*P^-1 can be evaluated efficiently. More...
subroutine	matvecprod5 (a, v, c)
	Computes matrix times vector (n=5). More...

Function/Subroutine Documentation

real(rtype) function comptheta	(	real(rtype), intent(in)	gam,
		real(rtype), intent(in)	c,
		real(rtype), intent(in)	q2
	)

Parameters

gam	ratio of specific heats
c	speed of sound
q2	total velocity squared

subroutine cons2prim	(	real(rtype), dimension(5), intent(in)	wvec,
		real(rtype), dimension(5), intent(in)	wpvec,
		real(rtype), intent(in)	H,
		real(rtype), intent(in)	q2,
		real(rtype), intent(in)	theta,
		real(rtype), intent(in)	rhoT,
		real(rtype), intent(in)	hp,
		real(rtype), intent(in)	hT,
		real(rtype), dimension(5,5), intent(out)	pmat1
	)

Parameters

wvec	vector of conservative variables
wpvec	vector of primitive variables
H	total enthalpy
q2	total velocity squared
theta	preconditioning parameter
rhoT	derivative of density wrp. to temperature
hp	derivative of enthalpy wrp. to pressure
hT	derivative of enthalpy wrp. to temperature
pmat1	inverse of matrix P

subroutine lefteigenvec	(	real(rtype), dimension(5), intent(in)	wvec,
		real(rtype), dimension(5), intent(in)	wpvec,
		real(rtype), dimension(3), intent(in)	nvec,
		real(rtype), intent(in)	V,
		real(rtype), intent(in)	theta,
		real(rtype), intent(in)	rhop,
		real(rtype), intent(in)	rhoT,
		real(rtype), intent(in)	hp,
		real(rtype), intent(in)	hT,
		real(rtype), dimension(5,5), intent(out)	evl
	)

Parameters

wvec	vector of conservative variables
wpvec	vector of primitive variables
nvec	components of the unit normal vector
V	contravariant velocity
theta	preconditioning parameter
rhop	derivative of density wrp. to pressure
rhoT	derivative of density wrp. to temperature
hp	derivative of enthalpy wrp. to pressure
hT	derivative of enthalpy wrp. to temperature
evl	matrix of left eigenvectors (T_p)^-1

subroutine matprodtp1_p1	(	real(rtype), dimension(5), intent(in)	wvec,
		real(rtype), dimension(5), intent(in)	wpvec,
		real(rtype), dimension(3), intent(in)	nvec,
		real(rtype), intent(in)	V,
		real(rtype), intent(in)	H,
		real(rtype), intent(in)	theta,
		real(rtype), intent(in)	rhop,
		real(rtype), intent(in)	rhoT,
		real(rtype), intent(in)	hp,
		real(rtype), intent(in)	hT,
		real(rtype), intent(in)	q2,
		real(rtype), dimension(5,5), intent(out)	mat
	)

Parameters

wvec	vector of conservative variables
wpvec	vector of primitive variables
nvec	components of the unit normal vector
V	contravariant velocity
H	total enthalpy
theta	preconditioning parameter
rhop	derivative of density wrp. to pressure
rhoT	derivative of density wrp. to temperature
hp	derivative of enthalpy wrp. to pressure
hT	derivative of enthalpy wrp. to temperature
q2	total velocity squared
mat	resulting matrix

subroutine matrixtimesinverse	(	real(rtype), dimension(5), intent(in)	wpvec,
		real(rtype), intent(in)	q2,
		real(rtype), dimension(5,5), intent(in)	amat,
		real(rtype), dimension(5,5), intent(in)	bmat,
		real(rtype), dimension(5,5), intent(out)	cmat
	)

Parameters

wpvec	vector of primitive variables
q2	total velocity squared
amat	matrix A
bmat	matrix B
cmat	resulting matrix C, i.e., C=A*B

subroutine matvecprod5	(	real(rtype), dimension(5,5), intent(in)	a,
		real(rtype), dimension(5), intent(in)	v,
		real(rtype), dimension(5), intent(out)	c
	)

Parameters

a	5x5 matrix A
v	vector v (length 5)
c	resulting vector c, i.e., c=A*v

subroutine prim2cons	(	real(rtype), dimension(5), intent(in)	wvec,
		real(rtype), dimension(5), intent(in)	wpvec,
		real(rtype), intent(in)	H,
		real(rtype), intent(in)	theta,
		real(rtype), intent(in)	rhoT,
		real(rtype), intent(in)	hp,
		real(rtype), intent(in)	hT,
		real(rtype), dimension(5,5), intent(out)	pmat
	)

Parameters

wvec	vector of conservative variables
wpvec	vector of primitive variables
H	total enthalpy
theta	preconditioning parameter
rhoT	derivative of density wrp. to temperature
hp	derivative of enthalpy wrp. to pressure
hT	derivative of enthalpy wrp. to temperature
pmat	matrix P

subroutine righteigenvec	(	real(rtype), dimension(5), intent(in)	wvec,
		real(rtype), dimension(5), intent(in)	wpvec,
		real(rtype), dimension(3), intent(in)	nvec,
		real(rtype), intent(in)	V,
		real(rtype), intent(in)	H,
		real(rtype), intent(in)	theta,
		real(rtype), intent(in)	rhop,
		real(rtype), intent(in)	rhoT,
		real(rtype), intent(in)	hp,
		real(rtype), intent(in)	hT,
		real(rtype), dimension(5,5), intent(out)	evr
	)

Parameters

wvec	vector of conservative variables
wpvec	vector of primitive variables
nvec	components of the unit normal vector
V	contravariant velocity
H	total enthalpy
theta	preconditioning parameter
rhop	derivative of density wrp. to pressure
rhoT	derivative of density wrp. to temperature
hp	derivative of enthalpy wrp. to pressure
hT	derivative of enthalpy wrp. to temperature
evr	matrix of right eigenvectors multiplied by G (G*T_p)