For the three-dimensional incompressible Navier-Stokes equations, we present a formulation featuring velocity, vorticity and helical density as independent variables. We find the helical density can be observed as a Lagrange multiplier corresponding to the divergence-free constraint on the vorticity variable, similar to the pressure in the case of the incompressibility condition for velocity. A...

We present a fully coupled three dimensional formulation based on arbitrary Lagrangian-Eulerian (ALE) approach with exact interface tracking for nonlinear fluid-structure interactions. This formulation is second order accurate in time and stable for very low mass ratios of O(10). The proposed formulation is an extension of the combined field with explicit interface (CFEI) presented in [1, 2] fo...

in this paper, a new enhanced version of the particle swarm optimization (pso) is presented. an important modification is made by adding probabilistic functions into pso, and it is named probabilistic particle swarm optimization (ppso). since the variation of the velocity of particles in pso constitutes its search engine, it should provide two phases of optimization process which are: explorati...

An absolutely stabilized finite element formulation for the Stokes problem is presented in this paper. This new formulation, which is nonsymmetric but stable without employment of any stability constant, can be regarded as a modification of the formulation proposed recently by Hughes and Franca in [8]. Optimal error estimates in L2-norm for the new stabilized finite element approximation of bot...

This paper proposes a numerical simulation of the incompressible viscous flows with hyper dissipation using Femlab. We propose two variational formulations to solve this problem: the primal and the mixed formulations. For the first one, a biharmonic formulation for the velocity and the pressure is used. The second one uses a mixed formulation where the laplacian of the velocity, the velocity an...

Previous work in haptics surface tracing for virtual prototyping and surface design applications has used a point model for virtual finger-surface interaction. We extend this tracing method for surface-to-surface interactions. A straightforward extension of the point-surface formulation to surface-surface can yield extraneous, undesirable solutions, although we rework the formulation to yield m...

The stress-velocity formulation of the stationary Stokes problem allows an Arnold–Winther mixed finite element formulation with some superconvergent reconstruction of the velocity. This local postprocessing gives rise to two reliable a posteriori error estimators which recover optimal convergence order for the stress error estimates. The theoretical results are investigated in numerical benchma...

This paper addresses the control of robotic manipulators using the velocity field approach. Instead of the usual specification in motion robot control via desired position trajectories depending on time, the specification in the velocity field control formulation is given through a desired velocity vector field as a function of actual position regardless of time. This approach is useful for con...

We evaluate the stabilized three-field stress-velocity-pressure Galerkin/LeastSquares finite element formulation for viscoelastic fluids, using a benchmark problem of Oldroyd-B flow past a cylinder at various Weissenberg numbers. To address the issue of weak consistency exhibited by low-order velocity interpolations in the context of stabilized formulations, we also employ velocity gradient rec...