# Tag Info

5

The data in the SPH format is perfectly "physically sensible", you just need to know how to interpret it. In the SPH formulation, you can compute any particle quantity $A$ at any given point using $$A(\mathbf r) = \sum_j m_j \frac{A_j}{\rho_j} W(\|\mathbf r-\mathbf r_j\|,h_j).$$ Where $\mathbf r$ is the target point, e.g. a node on your grid, and $\mathbf ... 4 There are of course many aspects to solving coupled problems (discretizations, solvers, ...). Assuming you are interested in solvers and preconditioners, then lectures 37 and 38 at http://www.math.tamu.edu/~bangerth/videos.html may have something for you. (Disclaimer: these are my own lectures.) 4 Finite element methods for coupled systems are treated for example in Chapter 18 of The Finite Element Method: Its Basis and Fundamentals by Zienkiewicz, Taylor and Zhu. It might also be useful to search for literature on particular coupled systems (presumably there's a specific one you are interested in) such as those modeling fluid-structure interaction or ... 3 Do you wish to model the two-way coupled solid-fluid flows or you wish to carry out PIV or tracking on particle images? If you wish to model the two-way coupled solid-fluid flows, there are numerous type of models are that valid, most notably Euler-Euler approaches or Euler-Lagrange (CFD-DEM unresolved or resolved) approaches. Euler-Euler approaches are ... 3 The short answer to your question is that it works because of the Zassenhaus formula. Briefly, if$A$and$B$are linear operators, then $$e^{t(A + B)} = e^{tA}e^{tB}e^{-\frac{t^2}{2}[A, B]}\cdot\ldots$$ where the ellipses denote terms of higher order in$t\$. If both parts of your dynamics are linear, then for small enough timesteps you can split the ...

3

For linear problems of size ~1000, you can't beat a direct solver by trying to use an iterative solver. For problems of this size, it also doesn't really matter. If your problem was any bigger, I would recommend you watch/listen lectures 34 and 38 of the course I recorded this spring: http://www.math.tamu.edu/~bangerth/videos.html .

2

A new resource for high-order splitting schemes that lists quite a few can be found here: http://www.asc.tuwien.ac.at/~winfried/splitting/

2

The strategy would really be very similar -- partition your matrix and vectors into "blocks" that correspond to the variables living on the different phases. The difference is really just that the coupling isn't for all variables at the same location, but only for the variables located on different phases at the same points on interfaces. That means that ...

1

Computational fluid-structure interaction is challenging endeavour. The type of coupling algorithm you need to employ depends on the type of the problem you want to solve. It is important to understand the difficulties associated with simulating different kinds of FSI problems. You may refer to my recent presentation on the topic for the details. Title: ...

1

Finite element method is used to change the boundary value problem, with an infinite number of unknowns, into a system of algebraic equations with a finite number of degrees of freedom (DOFs). For example, the response of the deformable body, which conveniently is described by partial diffrenetial equation (PDE), using finite element method is transformed ...

1

People typically agree that the monolithic approach is the conceptually better one, but of course more difficult to implement. If you want to use a code that already does most of what you need, I would suggest to look at this paper and its accompanying code: http://journals.ub.uni-heidelberg.de/index.php/ans/issue/view/1244

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