954 research outputs found
On Meshfree GFDM Solvers for the Incompressible Navier-Stokes Equations
Meshfree solution schemes for the incompressible Navier--Stokes equations are
usually based on algorithms commonly used in finite volume methods, such as
projection methods, SIMPLE and PISO algorithms. However, drawbacks of these
algorithms that are specific to meshfree methods have often been overlooked. In
this paper, we study the drawbacks of conventionally used meshfree Generalized
Finite Difference Method~(GFDM) schemes for Lagrangian incompressible
Navier-Stokes equations, both operator splitting schemes and monolithic
schemes. The major drawback of most of these schemes is inaccurate local
approximations to the mass conservation condition. Further, we propose a new
modification of a commonly used monolithic scheme that overcomes these problems
and shows a better approximation for the velocity divergence condition. We then
perform a numerical comparison which shows the new monolithic scheme to be more
accurate than existing schemes
Finite length effects in Taylor-Couette flow
Axisymmetric numerical solutions of the unsteady Navier-Stokes equations for flow between concentric rotating cyclinders of finite length are obtained by a spectral collocation method. These representative results pertain to two-cell/one-cell exchange process, and are compared with recent experiments
A FIC-based stabilized finite element formulation for turbulent flows
We present a new stabilized finite element (FEM) formulation for incompressible flows based on the Finite
Increment Calculus (FIC) framework. In comparison to existing FIC approaches for fluids, this formulation
involves a new term in the momentum equation, which introduces non-isotropic dissipation in the direction of
velocity gradients. We also follow a new approach to the derivation of the stabilized mass equation, inspired by
recent developments for quasi-incompressible flows. The presented FIC-FEM formulation is used to simulate
turbulent flows, using the dissipation introduced by the method to account for turbulent dissipation in the style
of implicit large eddy simulation.Peer ReviewedPostprint (author's final draft
Modeling electrochemical systems with weakly imposed Dirichlet boundary conditions
Finite element modeling of charged species transport has enabled analysis,
design, and optimization of a diverse array of electrochemical and
electrokinetic devices. These systems are represented by the
Poisson-Nernst-Planck equations coupled with the Navier-Stokes equation, with a
key quantity of interest being the current at the system boundaries. Accurately
computing the current flux is challenging due to the small critical dimension
of the boundary layers (small Debye layer) that require fine mesh resolution at
the boundaries. We resolve this challenge by using the
Dirichlet-to-Neumanntransformation to weakly impose the Dirichlet conditions
for the Poisson-Nernst-Planck equations. The results obtained with weakly
imposed Dirichlet boundary conditions showed excellent agreement with those
obtained when conventional boundary conditions with highly resolved mesh we
reemployed. Furthermore, the calculated current flux showed faster mesh
convergence using weakly imposed conditions compared to the conventionally
imposed Dirichlet boundary conditions. We illustrate the approach on canonical
3D problems that otherwise would have been computationally intractable to solve
accurately. This approach substantially reduces the computational cost of
model-ing electrochemical systems.Comment: 24 pages, 14 figure
Improvement in Computational Fluid Dynamics Through Boundary Verification and Preconditioning
This thesis provides improvements to computational fluid dynamics accuracy and ef- ficiency through two main methods: a new boundary condition verification procedure and preconditioning techniques. First, a new verification approach that addresses boundary conditions was developed. In order to apply the verification approach to a large range of arbitrary boundary condi- tions, it was necessary to develop unifying mathematical formulation. A framework was developed that allows for the application of Dirichlet, Neumann, and extrapolation bound- ary condition, or in some cases the equations of motion directly. Verification of boundary condition techniques was performed using exact solutions from canonical fluid dynamic test cases. Second, to reduce computation time and improve accuracy, preconditioning algorithms were applied via artificial dissipation schemes. A new convective upwind and split pressure (CUSP) scheme was devised and was shown to be more effective than traditional precon- ditioning schemes in certain scenarios. The new scheme was compared with traditional schemes for unsteady flows for which both convective and acoustic effects dominated. Both boundary conditions and preconditioning algorithms were implemented in the context of a strand grid solver. While not the focus of this thesis, strand grids provide automatic viscous quality meshing and are suitable for moving mesh overset problems
On Coupling a Lumped Parameter Heart Model and a Three-Dimensional Finite Element Aorta Model
Aortic flow and pressure result from the interactions between the heart and arterial system. In this work, we considered these interactions by utilizing a lumped parameter heart model as an inflow boundary condition for three-dimensional finite element simulations of aortic blood flow and vessel wall dynamics. The ventricular pressure–volume behavior of the lumped parameter heart model is approximated using a time varying elastance function scaled from a normalized elastance function. When the aortic valve is open, the coupled multidomain method is used to strongly couple the lumped parameter heart model and three-dimensional arterial models and compute ventricular volume, ventricular pressure, aortic flow, and aortic pressure. The shape of the velocity profiles of the inlet boundary and the outlet boundaries that experience retrograde flow are constrained to achieve a robust algorithm. When the aortic valve is closed, the inflow boundary condition is switched to a zero velocity Dirichlet condition. With this method, we obtain physiologically realistic aortic flow and pressure waveforms. We demonstrate this method in a patient-specific model of a normal human thoracic aorta under rest and exercise conditions and an aortic coarctation model under pre- and post-interventions
High-Reynolds-number wall-modelled large eddy simulations of turbulent pipe flows using explicit and implicit subgrid stress treatments within a spectral element solver
We present explicit and implicit large eddy simulations for fully developed turbulent pipe flows using a continuous-Galerkin spectral element solver. On the one hand, the explicit stretched-vortex model (by Misra & Pullin [45] and Chung & Pullin [14]), accounts for an explicit treatment of unresolved stresses and is adapted to the high-order solver. On the other hand, an implicit approach based on a spectral vanishing viscosity technique is implemented. The latter implicit technique is modified to incorporate Chung & Pullin virtual-wall model instead of relying on implicit dissipative mechanisms near walls. This near-wall model is derived by averaging in the wall-normal direction and relying in local inner scaling to treat the time-dependence of the filtered wall-parallel velocity. The model requires space-time varying Dirichlet and Neumann boundary conditions for velocity and pressure respectively. We provide results and comparisons for the explicit and implicit subgrid treatments and show that both provide favourable results for pipe flows at Re_Ď„ = 2Ă—10^3 and Re_Ď„ = 1.8Ă—10^5 in terms of turbulence statistics. Additionally, we conclude that implicit simulations are enhanced when including the wall model and provide the correct statistics near walls
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