By G. R. Liu, M. B. Liu

Книга Smoothed Particle Hydrodynamics: A Meshfree Particle technique Smoothed Particle Hydrodynamics: A Meshfree Particle MethodКниги Физика Автор: G. R. Liu, M. B. Liu Год издания: 2003 Формат: pdf Издат.:World clinical Publishing corporation Страниц: 472 Размер: 20,9 Mb ISBN: 9812384561 Язык: Английский0 (голосов: zero) Оценка:ReviewsComputational MechanicsOne of the original function of the booklet is its emphasis at the desktop implementation and coding of SPH approach. Zentralblatt MATH… can function an exceptional begin to successfully research, try, instruction and advance such new tools.

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**Example text**

The flux of mass, momentum and energy across mesh cell boundaries are simulated to compute the distribution of mass, velocity, energy, etc. in the problem domain. The shape and volume of the mesh cell remain unchanged in the entire process of the computation. 5 Eulerian mesh/cells/grids for a shaped charge detonation simulation. The mesh/grid is fixed in space and does not move or deform with time. The material moves/flows across the fixed mesh cells. Since the Eulerian grid is fixed in space and with time, large deformations in the object do not cause any deformations in the mesh itself and therefore do not cause the same kind of numerical problems as in the Lagrangian grid-based methods.

It is done by replacing the integration in the integral representation of the field function and its derivatives with summations over all the corresponding values at the neighboring particles in a local domain called the support domain. {Compact support) The particle approximation is performed at every time step, and hence the use of the particles depends on the current local distribution of the particles. {Adaptive) The particle approximations are performed to all terms related to field functions in the PDEs to produce a set of ODEs in discretized form with respect to time only.

4) leads to 38 Smoothed Particle Hydrodynamics < J \X) >— \u\X) + j (X)(X — x)-t-r((x n X) )\w \x — x ,njax =-f(x)jW(x-x',h)dx' (2g) n +/'(x) \(x' - x)W(x - x', h)dx' + r(h2) n where r stands for the residual. 10) From the above equation, it can be seen that, in the SPH method, the integral representation or kernel approximation of a function is of second order accuracy. However, this kernel approximation is not necessarily of second order accuracy if the smoothing function is not an even function, or if the normalization condition is not satisfied.