MegaCads Help: Elliptic Grid Smoothing (P. Niederdrenk)

2D Control/Smoothing (Niederdrenk)

The 2d elliptic control/smoothing function was developed and now enhanced by Dr. P. Niederdrenk for grids with low and high aspect ratio cells (Navier-Stokes). It allows the angle and orthogonality control for a user specified number of grid lines. The main features are :

Grid generation from weighed superposition of line-wise central target points
no control functions involved
Dirichlet BC
control relative to surfaces (i,j=const) being fixed (boundaries) or evolving with the solution
controlled are spacings and angles (unit tangents to the grid lines or orthogonality requirement)
spacings may be taken from algebraic grid or from the boundaries with subsquent interpolation into the field
either unit tangents from algebraic grid (ic,jc =2) or other angle specifications(ic,jc .ne. 2)
limiter on grid control to avoid grid overlap
off-boundary spacing correction for unfavourable aspect ratio
automatized relaxation

If the current working surface is a Coons surface the grid will be projected otherwise the grid z coordinate has to be zero. The projection may strongly affect the quality of the grid.

The user should modify the following main parameter:

iter: total number of outer iterations (1...1000)
boundary condition imin: 1=straight line, 2=unit direction, 3= normal to imin
boundary condition imax: 1=straight line, 2=unit direction, 3= normal to imin
boundary condition jmin: 1=straight line, 2=unit direction, 3= normal to imin
boundary condition jmax: 1=straight line, 2=unit direction, 3= normal to imin
I-direction spacing objective: 0=from start grid , 1=interpolated from boundaries
J-direction spacing objective: 0=from start grid , 1=interpolated from boundaries
imin no of lines for control (3...imax-imin)
imax no of lines for control (3...imax-imin)
jmin no of lines for control (3...jmax-jmin)
jmax no of lines for control (3...jmax-jmin)
grid dimensions imin,imax,jmin,jmax; subdomains can be controlled

Advanced parameters:

epsrat: stops iterations for relative changes (0.1)
omega: maximal under/over-relaxation coefficient 0.9/1.8
I-direction Laplace control: Weight on control in the interior relative to Laplace (0.0 ... 1.0)
J-direction Laplace control: iWeight on control in the interior relative to Laplace (0.0 ... 1.0)
jacobi: 0:Gauss-Seidel local omega, 1:Jacobi const.omega, 2:Jacobi loc.omega
I-direction nwarci 0/1: control weight in comput./physical space (phys. space more exact; comp. space smoother)
J-direction nwarcj 0/1: control weight in comput./physical space (phys. space more exact; comp. space smoother)
I-direction ndecayi: 0/1: strong/weak initial decay of control
J-direction ndecayj: 0/1: strong/weak initial decay of control
I-direction alpi: Exponent for decay of control (2.0)
J-direction alpj: Exponent for decay of control (2.0)
nLimNegativeVol : 0/1 no/with limiter; automatically switched on after n iterations, when negative volumes appear
nVolCheckIter : volume check after n iterations
nCorrecAspectRatioBC: 0/1 correction of ar-effect on off-boundary spacing

Usage:

Select 2d grid entity
Choose number of iterations
Choose number of lines for control in i,j direction
Change default parameter if necessary

Result:

2d grid entity

Script process and parameter: smooth_elliptic2_pn

Index of 2d grid entity
iter, Number of iterations
dEpsrat
dOmega
dLaplaceControl_I
dLaplaceControl_J
nSpacingObjective_I
nSpacingObjective_J
nIcu, bnd cond imin
nIcd, bnd cond imax
nJcu, bnd cond jmin
nJcd, bnd cond jmax
Block, Subblock imin
Block, Subblock imax
Block, Subblock jmin
Block, Subblock jmax
no of lines for control imin
no of lines for control imax
no of lines for control jmin
no of lines for control jmax
control weight comput./physical space i-direction (0/1)
control weight comput./physical space j-direction (0/1)
strong/weak decay of control (0/1), i-direction
strong/weak decay of control (0/1), j-direction
decay exponent, i-direction (2.0)
decay exponent, j-direction (2.0)
nLimNegativeVol: 0/1 no/with limiter; automatically switched on after ..iterations, when negative volumes appear
nCorrecAspectRatioBC: 0/1 correction of ar-effect on off-boundary spacing
nJacobi: 0:Gauss-Seidel local omega, 1:Jacobi const.omega, 2:Jacobi loc.omega
nIcm: 0 for internal faces in 3d only
nJcm: 0 for internal faces in 3d only

3D Control/Smoothing (Niederdrenk)

The user can control the spacing and orthogonality of the grid easily by specifying boundary conditions on six faces (spacing, orthogonality, and no of lines for control). The main features are :

Grid generation from weighted superposition of line-wise objective central points
no control functions involved
Dirichlet BC
control relative to surfaces (i,j,k=const) being fixed (boundaries) or evolving with the solution
controlled are spacings and angles (unit tangents to the grid lines or orthogonality requirement or partial orthogonality requirement by projection onto a grid surface)
spacings may be taken from algebraic grid or from the boundaries with subsquent interpolation into the field
either unit tangents from algebraic grid (ic,jc,kc =2) or other angle specifications(ic,jc,kc .ne. 2)
in an interior domain to be defined by the user
equally weighted superpositions from up- and downstream objectives or additionally Laplace smoothing of v(i,j,k,3)
controll from the six boundary faces and from up to 3 internal faces in each i,j,k direction possible

Numerical parameter:

iter: total number of outer iterations (1...1000)
boundary condition i,j,k min/max: 1=straight line, 2=unit direction, 3= normal to face, 4= normal to edge m+1, 5= normal to edge m+2
I,J,K-direction spacing objective: 0=from start grid , 1=interpolated from boundaries
i,j,k, min/max no of lines for control (3...max-min)
grid dimensions ij,k, min/max; subdomains can be controlled

Advanced parameters:

epsrat: stops iterations for relative changes (0.1)
omega: maximal under/over-relaxation coefficient 0.9/1.8
I,J,K-direction Laplace control: Weight on control in the interior relative to Laplace (0.0 ... 1.0)
jacobi: 0:Gauss-Seidel local omega, 1:Jacobi const.omega, 2:Jacobi loc.omega
I,J,K-direction nwarci 0/1: control weight in comput./physical space (phys. space more exact; comp. space smoother)
I,J,K-direction ndecayi: 0/1: strong/weak initial decay of control
I,J,K-direction : Exponent for decay of control (2.0)
nLimNegativeVol : 0/1 no/with limiter; automatically switched on after n iterations, when negative volumes appear
nVolCheckIter : volume check after n iterations
nCorrecAspectRatioBC: 0/1 correction of ar-effect on off-boundary spacing
I,J,K internal control faces (max 3 in each direction)

Usage:

Select 3d grid entity
Choose number of iterations
Choose number of lines for control in i,j,k direction
Change default parameter if necessary

Result:

3d grid entity

Script process and parameter: smooth_elliptic3_pn_aver

Index of 3d grid entity
iter, Number of iterations
dEpsrat
dOmega
dLaplaceControl_I
nSpacingObjective_I
nIcu, bnd cond imin
nIcd, bnd cond imax
nJcu, bnd cond jmin
nJcd, bnd cond jmax
nKcu, bnd cond kmin
nKcd, bnd cond kmax
Block, Subblock imin
Block, Subblock imax
Block, Subblock jmin
Block, Subblock jmax
Block, Subblock kmin
Block, Subblock kmax
no of lines for control imin
no of lines for control imax
no of lines for control jmin
no of lines for control jmax
no of lines for control kmin
no of lines for control kmax
control weight comput./physical space i-direction (0/1)
control weight comput./physical space j-direction (0/1)
control weight comput./physical space k-direction (0/1)
strong/weak decay of control (0/1), i-direction
strong/weak decay of control (0/1), j-direction
strong/weak decay of control (0/1), k-direction
decay exponent, i-direction (2.0)
decay exponent, j-direction (2.0)
decay exponent, k-direction (2.0)
dLaplaceControl_J
dLaplaceControl_K
nSpacingObjective_J
nSpacingObjective_K
nLimNegativeVol: 0/1 no/with limiter; automatically switched on after ..iterations, when negative volumes appear
nCorrecAspectRatioBC: 0/1 correction of ar-effect on off-boundary spacing
nJacobi: 0:Gauss-Seidel local omega, 1:Jacobi const.omega, 2:Jacobi loc.omega
nIcm: no. of internal faces (0...3)
nJcm: no. of internal faces (0...3)
nKcm: no. of internal faces (0...3)
Face I_1_up
Face I_1
Face I_1_down
Face I_2_up
Face I_2
Face I_2_down
Face I_3_up
Face I_3
Face I_3_down
Face J_1_up
Face J_1
Face J_1_down
Face J_2_up
Face J_2
Face J_2_down
Face J_3_up
Face J_3
Face J_3_down
Face K_1_up
Face K_1
Face K_1_down
Face K_2_up
Face K_2
Face K_2_down
Face K_3_up
Face K_3
Face K_3_down

2D Surface Control/Smoothing (Niederdrenk)

The 2d elliptic control/smoothing function for surfaces was developed by Dr. P. Niederdrenk for grids with low and high aspect ratio cells (Navier-Stokes). It has nearly the same features as the previous described 2d function, but now after a user specified number of iterations the grid is projected to the surface several times. Additional features are :

projection to the working surface during iterations
smoothing of non-planar grids in 3d space

If the current working surface is a Coons surface the grid will be projected during the iterations. The resulting grid is mainly indepented of the underlaying Coons surface.

The user should modify the following main parameter:

iter: total number of outer iterations (1...1000)
iter_project: number of iterations after projection is applied
omega: maximal under/over-relaxation coefficient 0.9/1.8
boundary control type (No/Angle/Angle+Spacing)
no of lines for control at imin (3...imax-imin)
no of lines for control at imax (3...imax-imin)
no of lines for control at jmin (3...jmax-jmin)
no of lines for control at jmax (3...jmax-jmin)
decay exponent for spacing control, i-direction (default 2.0)
decay exponent for spacing control, j-direction (default 2.0)
decay exponent for orthogonality control, i-direction (default 2.0)
decay exponent for orthogonality control, j-direction (default 2.0)

Usage:

Select 2d grid entity
Choose number of iterations
Choose number of iterations after which projection is applied

Result:

2d grid entity

Script process and parameter: smooth_elliptic2_pn_surf

Index of 2d grid entity
dOmega
nIterations_out
nIterations_min (=0)
nIterations_inner (=1)
nIterations_project
nSpacingObjective (=2)
nCurveMode (=0)
nControl
nMode (=5)
CorrectWeight (=2.0)
nCurveSpac (=1)
nIcu
nIcd
nJcu
nJcd
dDecayExpSpac_I
dDecayExpSpac_J
dDecayExpOrth_I
dDecayExpOrth_J