It combines a smoothing procedure including bicubic B-spline patches together with a Lagrange multiplier based contact strategy within an explicit time-marching integration procedure preferred for its versatility.
The method combines an explicit time-marching algorithm, previously developed for Bose Einstein condensates in a harmonic or optical-lattice potential, with a particle-in-cell approach to the equation of motion for the one-body Wigner distribution function in the cold-atom cloud.
The computational results obtained by means of an explicit time marching solver are compared with experimental outcomes for validation purposes.
As a result of this, the allowable time step in an explicit time marching algorithm is O N-2) which, in many cases, is much belO N-2e time step dictated by the physics of the PDE.
A simple isoparametric finite element formulation based on a higher-order displacement model for dynamic analysis of multi-layer symmetric composite plates is presented with an explicit time marching scheme.
It is demonstrated through both analysis and corroborative numerical experiments that: (1 ) It is quite feasible to incorporate, efficiently, a two-equation k-ϵ turbulence model in an explicit time marching scheme, provided certain numerical stability constraints are enforced.
Traditionally, micro macro simulations have been performed using simple explicit time-marching algorithms, which lack the desirable stability of implicit methods.
The time-dependent problem is solved using the explicit time marching process introduced in Mesquita and Coda (2001 , 2002 2003).
Further, when used as the spatial discretization for time-dependent partial differential equations in combination with explicit time-marching, prolate functions allow a longer stable timestep than Legendre polynomials.
The artificial compressibility method (ACM) [6] introduces a time derivative of the pressure into the incompressible form of the continuity equation creating a coupled closed hyperbolic system that does not require a Poisson equation solution and allows for explicit time-marching and localized stencil numerical methods.
