Civil Engineering Reference
In-Depth Information
Figure 9.4
Velocity vectors at convergence from Program 9.1 example
Program 9.2 Analysis of the plane steady state Navier-Stokes equation using 8-node
rectangular quadrilaterals for velocities coupled to 4-node rectangular quadrilaterals
for pressures. Mesh numbered in
x
-or
y
-direction. Freedoms numbered in the order
u
-
p
-
v
. Element-by-element solution using BiCGStab(l) with no preconditioning. No
global matrix assembly.
PROGRAM p92
!--------------------------------------------------------------------------
! Program 9.2 Analysis of the plane steady state Navier-Stokes equation
! using 8-node rectangular quadrilaterals for velocities
! coupled to 4-node rectangular quadrilaterals for pressures.
! Mesh numbered in x- or y-direction. Freedoms numbered in the
! order u-p-v. Element by element solution using BiCGStab(l).
! with no preconditioning. No global matrix assembly,
!--------------------------------------------------------------------------
USE main; USE geom; IMPLICIT NONE
INTEGER,PARAMETER::iwp=SELECTED_REAL_KIND(15)
INTEGER::cg_iters,cg_limit,cg_tot,ell,fixed_freedoms,i,iel,iters,j,k,
&
limit,ndim=2,nels,neq,nip=4,nn,nod=8,nodf=4,nodof=3,nr,ntot=20,nxe,nye
REAL(iwp)::alpha,beta,cg_tol,det,error,gama,kappa,norm_r,omega,
&
one=1.0_iwp,penalty=1.e5_iwp,pt5=0.5_iwp,rho,rho1,r0_norm,tol,ubar,
&
vbar,visc,x0,zero=0.0_iwp
CHARACTER(LEN=15)::element='quadrilateral'
LOGICAL::converged,cg_converged
!------------------------dynamic arrays------------------------------------
INTEGER,ALLOCATABLE::g(:),g_g(:,:),g_num(:,:),nf(:,:),no(:),node(:),
&
num(:),sense(:)
REAL(iwp),ALLOCATABLE::b(:),coord(:,:),coordf(:,:),c11(:,:),c12(:,:), &
c21(:,:),c23(:,:),c32(:,:),der(:,:),derf(:,:),deriv(:,:),derivf(:,:), &
diag(:),fun(:),funf(:),gamma(:),gg(:,:),g_coord(:,:),hh(:,:),jac(:,:), &
kay(:,:),ke(:,:),loads(:),nd1(:,:),nd2(:,:),nfd1(:,:),nfd2(:,:),
&
