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3D flow on a 2-D cartesian grid

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Old   February 10, 2008, 11:36
Default 3D flow on a 2-D cartesian grid
  #1
jinwon park
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Currently, I need to solve a real 3-D compressible flow induced by explosions. Since 3-D simulations are costly, I hope that a reduced 2-D one(or somewhat else) can solve such complex real flows. Could anyone give insights to enhance computing cost?

In the literature, people used 2-D axisymmetric model but I thought this is not applicable to mine where a spherical gas bubble is initially embedded on a grid. I could not believe they obtained physically acceptable results.

Can anyone explain the way to solve 3-D real flows on a 2D grid?

Thanks in advance.
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Old   February 10, 2008, 15:56
Default Re: 3D flow on a 2-D cartesian grid
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otd
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Whether 2D axisymmetric is reasonable or not depends the problem - at least that's my first thought.

If the charge is small relative to the problem size/time of interest, you might treat it as a point source of mass and momentum at ignition.

If you have a 'torpedo' (cylinder) of explosive, such as might be used in an underground well bore hole to fracture the stratum and release oil or natural gas, treat it as a line source on the axis of the bore hore.

An above-ground (point charge) explosion might be axisymmetric if the ground is flat. Shocks would (be assumed to) reflect from the ground in axisymmetric fashion about a vertical axis passing through the initial location of the charge.

After these more-or-less obvious cases, 3D perhaps becomes more necessary. What configuration are you considering?

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Old   February 10, 2008, 17:51
Default Re: 3D flow on a 2-D cartesian grid
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jinwon park
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I am considering the case where a charge is placed above the plate. The charge is usually a spherical-shape charge. If we consider axisymmetric configurations, it might not be right.
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Old   February 10, 2008, 19:54
Default Re: 3D flow on a 2-D cartesian grid
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Ananda Himansu
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Every spherically symmetric 3-D solution is also axisymmetric. It is axisymmetric about every axis passing through the center of spherical symmetry. The introduction of an infinite plate will eliminate the spherical symmetry, but the solution should still be axisymmetric about an axis passing through the center of the spherical charge and perpendicular to the plate.
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Old   February 10, 2008, 20:10
Default Re: 3D flow on a 2-D cartesian grid
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jinwon park
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Based on my experience, it is not since axisymmetric flows are symmetry only against one axis. So, if one sets a circle which is identical to a spherical charge in 2-D, it represents a tube in real 3-dimensions. Could you make sure me what you mentioned before?

Thanks in advance!
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Old   February 11, 2008, 01:27
Default Re: 3D flow on a 2-D cartesian grid
  #6
Hafidz
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unless the symmetrical axis runs right through the sphere...

Hafidz
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Old   February 11, 2008, 02:02
Default Re: 3D flow on a 2-D cartesian grid
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Ananda Himansu
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I think otd, Hafidz and I have already described similar situations. I am unclear as to what your exact geometry is. You mention a spherical gas bubble in your first post. Is that the explosive charge?

(1) A purely spherical explosion in an infinite medium is in particular axisymmetric at every instant about every axis passing through the center of spherical symmetry. It has greater symmetry than just axisymmetry, and in fact requires just one spatial coordinate (the radial one of spherical coordinates) as the independent variable (in addition to time), plus of course the origin.

(2) A purely cylindrical explosion from an infinite cylinder of charge into an infinite medium is axisymmetric at every instant about the axis of the cylinder. Its description requires one spatial coordinate (the radial one of cylindrical coords), plus the axis of the cylinder.

(3) A spherical charge at any distance from an infinite impenetrable plane will yield an axisymmetric solution at every instant of time. The axis of symmetry passes through the center of the spherical charge and is perpendicular to the plane. The solution description requires two spatial coordinates, the radial and axial ones in the cylindrical coordinate system with the axis of symmetry as the cylindrical coord axis.

(4) A cylindrical charge perpendicular to an infinite impenetrable plane yields an axisymmetric solution at every instant of time. The axis of symmetry is the axis of the charge. The solution description requirement is the same as in (3) above.

(5) A cylindrical charge parallel to an infinite plane (or at any non-right-angle to it) produces a NON axisymmetric solution at every instant of time that requires all three spatial coordinates for its description.

(6) A finite plane with non-axisymmetric boundary but otherwise the same as cases (3) and (4) produces a non-axisymmetric (3-D) solution.

Again, would you please specify your case more precisely?
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Old   February 11, 2008, 05:28
Default Re: 3D flow on a 2-D cartesian grid
  #8
Ananda Himansu
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I forgot to mention, in case (5) if the infinite cylinder is actually parallel to the infinite plane, the solution though non-axisymmetric, is two-dimensional at every instant: it is the same in every spatial slice perpendicular to the axis of the cylinder (and the impenetrable plane).
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Old   February 11, 2008, 07:02
Default Re: 3D flow on a 2-D cartesian grid
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Rami
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Just a comment to be precise.

Even if the charge is spherical and the ground is flat, it is possible to have non-axisymmetric solution if the charge is initiated asymmetrically relative to the normal to the plane passing through the sphere center (asymmetric boundary condition). If this is not the case, and all boundary conditions are axisymmetric - an axisymmetric solution is reasonable.
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Old   February 11, 2008, 08:02
Default Re: 3D flow on a 2-D cartesian grid
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jinwon park
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To Rami, what is axisymmetric boundary condition?
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Old   February 11, 2008, 11:42
Default Re: 3D flow on a 2-D cartesian grid
  #11
Ananda Himansu
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This is certainly true. I was assuming that all initial and boundary conditions are symmetric about the appropriate axis, and precluding any symmetry-breaking via instabilities such as is likely to occur on a small scale in the real world.
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Old   February 12, 2008, 02:51
Default Re: 3D flow on a 2-D cartesian grid
  #12
Rami
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Axisymmetric = independent of the azimuthal angle (i.e., depends at most on the axial and radial coordinates).

Axisymmetric BC = the boundary conditions are independent of the azimuthal angle.

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