Numerical methods for solidification

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Numerical methods for solidification

• Kees Verhoeven

http//www.win.tue.nl/keesverh/presentations/pres
numlab.pdf
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Project Laser percussion drillingsee
http//www.win.tue.nl/keesverh/can be divided
in

• Melting
• Splashing
• Solidificationsee http//www.win.tue.nl/keesverh
  /presentations/presaday.ppt

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Solidification

• Unknowns
• Equations
• Conservation of mass
• Burgers equation
• Heat equation

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Numerics of solidification model(Software to be
found in NumLab oml-toolbox version 2.12)
FEM Sepran (Fortran)
SLM Burgers C
SLM Mass C
Software for boxed part is shown on next slide,
green arrows indicate usage of splines
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SLM-part verhoeven library

• Consists of
• MInit initialization of u and h
• MUpdateU SLM for Burgers equation
• MUpdateH SLM for mass equation
• These two specific implementations are typical
  for my
• research, but can be changed easily.
• MDFxLimiter defines the slope limiter function
  used in a SLM
• MIteration comprised of MDFxLimiter (2x),
  MUpdateU and MUpdateH

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SLM-part verhoeven library
Part of verhoeven-3d.sav.C, use of Mloop can be
seen in network.
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Side step generate MPEG using VTK-library
Part of verhoeven-3d-with-mpeg.sav.C
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Numerics of solidification model
FEM Sepran (Fortran)
SLM Burgers C
SLM Mass C
Green arrows indicate usage of splines
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Splines

• pppack (piecewise polynomial package)from
  www.netlib.org ( d/s)
• Above indicated part of pppack can be found in
  library pppackoperators
• This code is made available through wrapping
  Fortran source code, like in the oml-toolbox

cubspl.f to determine splines ppvalu.f to
evaluate spline interv.f needed for ppvalu
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pppackoperators/sources
For every .f a .h-file is made in the following
way. dcubspl.f subroutine dcubspl(tau, c, n,
ibcbeg, ibcend) dcubspl.h void
F77NAME(dcubspl)(const double tau, double c,
const int n, const int ibcbeg, const int
ibcend)
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pppackoperators/classes/NDSpline.cc

• constructor
• NDSpline(xi,C,ibcbeg,ibcend)
• uses definition of dcubspl.h
• void F77NAME(dcubspl)(_tau-gtgetValue(),
• c-gtgetValue(), n, ibcbeg, ibcend)
• operator() uses definition of dppvalu.h
• void F77NAME(dppvalu)(tau.getValue(),
• c.getValue(), l, k, x, _j)

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pppackoperators/modules/MDSpline.cc

• constructor now uses more user friendly input
  args
• MDSpline(z,x,xi,fxi,ibcbeg,begval,
• ibcend,endval)
• derives right C and calls NDSpline callback
• spline-gtcallback(xi,left_derivative,
• right_derivative)

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pppackoperators/modules/MDSpline.mh
Generates
x xi fxi ibcbeg begval ibcend endval
z
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Network showing usage of MDSpline
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Network showing usage of sampling
Note that evaluation points are fed to MDSpline
from below. (See spline-with-vis.sav.C)