Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Variational Time Integration Approach for Smoothed Particle
  Hydrodynamics Simulation of Fluids   Variational time integrators are derived in the context of discrete
mechanical systems. In this area, the governing equations for the motion of the
mechanical system are built following two steps: (a) Postulating a discrete
action; (b) Computing the stationary value for the discrete action. The former
is formulated by considering Lagrangian (or Hamiltonian) systems with the
discrete action being constructed through numerical approximations of the
action integral. The latter derives the discrete Euler-Lagrange equations whose
solutions give the variational time integrator. In this paper, we build
variational time integrators in the context of smoothed particle hydrodynamics
(SPH). So, we start with a variational formulation of SPH for fluids. Then, we
apply the generalized midpoint rule, which depends on a parameter $\alpha$, in
order to generate the discrete action. Then, the step (b) yields a variational
time integration scheme that reduces to a known explicit one if
$\alpha\in\{0,1\}$ but it is implicit otherwise. Hence, we design a fixed point
iterative method to approximate the solution and prove its convergence
condition. Besides, we show that the obtained discrete Euler-Lagrange equations
preserve linear momentum. In the experimental results, we consider artificial
viscous as well as boundary interaction effects and simulate a dam breaking set
up. We compare the explicit and implicit SPH solutions and analyze momentum
conservation of the dam breaking simulations.

18
The categories of this paper are: econ
4
The categories of this paper are: cond-mat
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph
27
The categories of this paper are: comp-gas
28
The categories of this paper are: alg-geom
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
24
The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn