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February 10, 2008, 11:36 
3D flow on a 2D cartesian grid

#1 
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Currently, I need to solve a real 3D compressible flow induced by explosions. Since 3D simulations are costly, I hope that a reduced 2D one(or somewhat else) can solve such complex real flows. Could anyone give insights to enhance computing cost?
In the literature, people used 2D 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 3D real flows on a 2D grid? Thanks in advance. 

February 10, 2008, 15:56 
Re: 3D flow on a 2D cartesian grid

#2 
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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 aboveground (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 moreorless obvious cases, 3D perhaps becomes more necessary. What configuration are you considering? 

February 10, 2008, 17:51 
Re: 3D flow on a 2D cartesian grid

#3 
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I am considering the case where a charge is placed above the plate. The charge is usually a sphericalshape charge. If we consider axisymmetric configurations, it might not be right.


February 10, 2008, 19:54 
Re: 3D flow on a 2D cartesian grid

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Every spherically symmetric 3D 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.


February 10, 2008, 20:10 
Re: 3D flow on a 2D cartesian grid

#5 
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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 2D, it represents a tube in real 3dimensions. Could you make sure me what you mentioned before?
Thanks in advance! 

February 11, 2008, 01:27 
Re: 3D flow on a 2D cartesian grid

#6 
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unless the symmetrical axis runs right through the sphere...
Hafidz 

February 11, 2008, 02:02 
Re: 3D flow on a 2D cartesian grid

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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 nonrightangle 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 nonaxisymmetric boundary but otherwise the same as cases (3) and (4) produces a nonaxisymmetric (3D) solution. Again, would you please specify your case more precisely? 

February 11, 2008, 05:28 
Re: 3D flow on a 2D cartesian grid

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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 nonaxisymmetric, is twodimensional at every instant: it is the same in every spatial slice perpendicular to the axis of the cylinder (and the impenetrable plane).


February 11, 2008, 07:02 
Re: 3D flow on a 2D cartesian grid

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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 nonaxisymmetric 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. 

February 11, 2008, 08:02 
Re: 3D flow on a 2D cartesian grid

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To Rami, what is axisymmetric boundary condition?


February 11, 2008, 11:42 
Re: 3D flow on a 2D cartesian grid

#11 
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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 symmetrybreaking via instabilities such as is likely to occur on a small scale in the real world.


February 12, 2008, 02:51 
Re: 3D flow on a 2D cartesian grid

#12 
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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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