Juan P. Pontaza

A least-squares finite element formulation for unsteady incompressible flows with improved velocity-pressure coupling

In the weak form Galerkin formulation for incompressible flows, the pressure has a well-understood role. At all times, it may be interpreted as a Lagrange multiplier that enforces the divergence-free constraint on the velocity field. This is not the case in least-squares formulations for incompressible flows, where the divergence-free constraint is enforced in a least-squares sense in a variational setting of residual minimization. Thus, the role of the pressure in a least-squares formulation is rather vague. We find that this lack of velocity-pressure coupling in least-squares formulations may induce spurious temporal pressure oscillations when using the non-stationary form of the equations. We present a least-squares formulation with improved velocity-pressure coupling, based on the use of a regularized divergence-free constraint. A first-order system least-squares (FOSLS) approach based on velocity, pressure and vorticity is used to allow the use of practical C0 element expansions in the finite element model. We use high-order spectral element expansions in space and second- and third-order time stepping schemes. Excellent conservation of mass and accuracy of computed pressure metrics are demonstrated in the numerical results.

Least-squares finite element models of two-dimensional compressible flows

We present numerical simulation results for the compressible Euler equations and compressible Navier-Stokes equations using least-squares finite element models. Alternative least-squares formulations are first exemplified by a Poisson problem and ideas extended to the Euler and Navier-Stokes equations. For the compressible Navier-Stokes equations we introduce velocity gradients and heat fluxes as additional primary variables to arrive at an equivalent first-order system. The least-squares models developed herein are found to be effective for the high- and low-speed compressible flow regime.

Three-Dimensional Numerical Simulations of Circular Cylinders Undergoing Two Degree-of-Freedom Vortex-Induced Vibrations

In an effort to gain a better understanding of vortex-induced vibrations (VIV), we present three-dimensional numerical simulations of VIV of circular cylinders. We consider operating conditions that correspond to a Reynolds number of 10 5 , low structural mass and damping (m*= 1.0, ζ*=0.005), a reduced velocity of U*=6.0, and allow for two degree-of-freedom (X and Y) motion. The numerical implementation makes use of overset (Chimera) grids, in a multiple block environment where the workload associated with the blocks is distributed among multiple processors working in parallel. The three-dimensional grid around the cylinder is allowed to undergo arbitrary motions with respect to fixed background grids, eliminating the need for grid regeneration as the structure moves on the fluid mesh.

NUMERICAL SIMULATION OF TUBULAR BLOWN FILM PROCESSING

A numerical simulation of the film blowing process was performed using the Runge-Kutta scheme. The kinematic and force balance equations governing the process are derived, and the constitutive model proposed by Cao and Campbell is utilized. The model accounts for liquidlike behavior at the freeze line; it alters the demarcation between liquidlike behavior and solidlike behavior from the suggested kinematicaly based constraint to a rheologically based constraint, the plastic-elastic transition (PET). The paper presents a detailed discussion on how the numerical models were developed and implemented. The numerical simulation was successful in duplicating Cao and Campbells results. Recommendations are made to gain some insight into the problem.A numerical simulation of the film blowing process was performed using the Runge-Kutta scheme. The kinematic and force balance equations governing the process are derived, and the constitutive model proposed by Cao and Campbell is utilized. The model accounts for liquidlike behavior at the freeze line; it alters the demarcation between liquidlike behavior and solidlike behavior from the suggested kinematicaly based constraint to a rheologically based constraint, the plastic-elastic transition (PET). The paper presents a detailed discussion on how the numerical models were developed and implemented. The numerical simulation was successful in duplicating Cao and Campbells results. Recommendations are made to gain some insight into the problem.

A spectral element least-squares formulation for incompressible Navier-Stokes flows using triangular nodal elements

We present a least-squares formulation for the numerical solution of incompressible flows using high-order triangular nodal elements. The Fekete points of the triangle are used as nodes and numerical integration is performed using tensor-product Gauss-Legendre rules in a collapsed coordinate system for the standard triangle. A first-order system least-squares (FOSLS) approach based on velocity, pressure, and vorticity is used to allow the use of practical C^0 element expansions in each triangle. The numerical results demonstrate spectral convergence for smooth solutions, excellent conservation of mass for steady and unsteady problems of the inflow/outflow type, and the flexibility of using triangles to partition domains where the use of quadrangles would be cumbersome or inefficient.

Prediction of Vortex-Induced Vibration Response of a Pipeline Span by Coupling a Viscous Flow Solver and a Beam Finite Element Solver

This paper describes a fluid-structure interaction (FSI) modeling approach to predict the vortex-induced vibration response of a pipeline span by coupling a three-dimensional viscous incompressible Navier–Stokes solver with a beam finite element solver in time domain. The pipeline span is modeled as an Euler–Bernoulli beam subject to instantaneous flow-induced forces and solved using finite element basis functions in space and an unconditionally stable Newmark-type discretization scheme in time. At each time step, the instantaneous incremental displacement is fed back to the fluid flow solver, where the position of the pipeline is updated to compute the resulting instantaneous flow field and associated flow-induced forces. Numerical predictions from the FSI model are compared to current tank experimental measurements of a pipeline span subject to uniform free-stream currents.