how to extend FSI 2D codes to 3D, need advises
How to make FSI codes with CFD and CCM in 3D case from the region of dynamics problems (explosions, impacts (km/sec) to vibration and static using the same Finite Volume simple, reliable and effective ? Need discussions and advices
Notations: High Order (second order) Godunov Type Finite Volume = HOGTFV Fluid Structure interaction = FSI Fluid Fluid interaction = FFI FLUID(state eq. #1) - Fluid(state eq. #2) Boundary = FFB Fluid - Solid Boundary = FSB Riemann's problem solver = RPS
at first about my experience and results on 2D case for CFD, CCM and FSI and FFI which I am going to use for 3D 2.1. for fluids
HOGTFV for moving Euler meshes on compact (3*3*3) stencil
with algorithms of monotonicity, density resolution, avoiding
of "carbuncle phenomena", the same order of accuracy (2 order) in
the boundary cells (free boundary and etc.) 2.2. for solids HOGTFV for moving Euler meshes on compact (3*3*3) stencil with algorithms of monotonicity, the same order of accuracy (2 order) in the boundary cells (free boundary and etc.), accuracy is enough even for vibration simulation of plates and shells, (no viscosity from the boundaries). For plasticity and viscosity effects and etc. in solids the splitting algorithm (Kukudzhanov approach) is used, which is enough to keep the same 2 order. 2.3. For FSI (fluid solids coupling) or FFI (fluid#1 fluid#2 coupling)
exact RPS is used (for FSI it is practically combining
of two RPS (for Tate state eq. for fluids and
elastic solver for Hook's law for solids) on the FSI boundary.
The algorithm of the FSI or FFI in 2D (Lagrangian on the boundaries of domains, Eulerian inside of each domain) 2.3.1. RPS are realized on all boundaries (FF, FS and etc) 2.3.2. all boundaries are moved in normal and tangent directions
with the velocities of these boundaries. 2.3.3. the new mesh is constructed on the new boundaries,
it means that on the normal direction Lagrangian movement of the
boundary line, for the tangent - Eulerian 2.3.4. the new Eulerian mesh in domains is constructed in accordance with the new mesh on the boundaries of the domains with the fluids and solids. 2.3.5. each domain with fluid or solids is solved in usual manner for
moving Eulerian mesh (step from old to new mesh)
advantages: good from acoustic case and vibration simulation
up to explosive and impact (several km/sec) problems
Problems: 1. even in 2D case if there are large deformation of the FFI or FSI,
sometimes it is a problem to construct the mesh inside the domain 2. the approximation error grows because the mesh is not rectangular
and changes a lot of 3. time step goes down from the stability requaments for such deformed mesh
How to go to 3D case for FFI and FSI?
This HOGTVF in 3D case is practically the same as for 2D
RPS also practically the same
For good accuracy for FSI and FFI
it is necessary to detect and follow the FFB and FSB
I see two ways of solution:
1 way: the same as in 2D
Lagrangian movement of the FFB and FSB surfaces
after appropriate RPS, then Eulirian movement mesh solver
(all 5 items of 2D)
Problems: 1. usual problem of 3D even generation of initial structured
or unstructured mesh, the mesh inside the domain is a function
of mesh on the domain's surfaces, this problem is huge and in
some case too complicated and takes a lot of time 2.movement of the FF and FS surfaces after RPS and construction of the new mesh on the surfaces is possible to solve 3. to construct the new mesh inside domains as a function of the new moved surfaces practically is impossible for a lot of cases. 4. to solve 3D for moving Euler is a problem for Gasdynamics may be it is OK but for Solids the volume calculation errors will completely destroy the solution (the small change of the density from the HOOK's state eq. will change the stress tensor a lot of),
So from my point of view it is impossible to make
3D codes similar to 2D with the same accuracy.
2 way: to use regular nonmoving rectangular Euler cubic mesh
for fluids and structures and to detect and follow the surfaces
of FFB or FSB
1. simple initial mesh generator, only surfaces
between FF and FS and the value of the cubic.
2. nonmoving mesh - simple integration of equations
3. the approximation error are in accordance with the accuracy
of the scheme
4. time step is OK
Problems: How to calculate the movement of the FF and FS surfaces? my opinion: it is necessary to calculate in local adaptive to surface mesh not only the movement of the FF or FS surface, but the cells, which are closed enough to the surfaces (taking into account the hypebolicity of the problem), for example 2 boundary layers parallel to FF or FS.
For this it is necessary 1. to construct local adaptive mesh on the FF or FS surface normal
to the surface, this local mesh is to be formaly enough for the accuracy of the scheme for 2 adjacent cells on the left and 2 adjacent on the right of the FF or FS 2. to interpolate from the cubic mesh the parameters with the appropriate accuracy to this local mesh and solve appropriate RPS and integrate all the adjacent cells like in 2D with the movement in normal to the surface direction. 3. solve the clean cells (which do not need the boundary conditions)
inside Fluids or Solids in nonmoving Euler 4. to construct the surfaces and to interpolate parameters
to the cubic's centers from the adjacent to the surface and clean cells.
I think in such manner it is possible to have the same accuracy
as in 2D and simulate from acoustic and vibration up
to explosions and meteor's (10km/sec) impacts and penetration.
need critiques, ideas and advices with the 3way and etc.
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