A CutFEM method for two-phase flow problems

In this article, we present a cut finite element method for two-phase Navier-Stokes flows. The main feature of the method is the formulation of a unified continuous interior penalty stabilisation approach for, on the one hand, stabilising advection and the pressure-velocity coupling and, on the other hand, stabilising the cut region. The accuracy of the algorithm is enhanced by the development of extended fictitious domains to guarantee a well defined velocity from previous time steps in the current geometry. Finally, the robustness of the moving-interface algorithm is further improved by the introduction of a curvature smoothing technique that reduces spurious velocities. The algorithm is shown to perform remarkably well for low capillary number flows, and is a first step towards flexible and robust CutFEM algorithms for the simulation of microfluidic devices

Extensions of High-order Flux Correction Methods to Flows With Source Terms at Low Speeds

A novel high-order finite volume scheme using flux correction methods in conjunction with structured finite difference schemes is extended to low Mach and incompressible flows on strand grids. Flux correction achieves high-order by explicitly canceling low-order truncation error terms in the finite volume cell. The flux correction method is applied in unstructured layers of the strand grid. The layers are then coupled together using a source term containing the derivatives in the strand direction. Proper source term discretization is verified. Strand-direction derivatives are obtained by using summation-by-parts operators for the first and second derivatives. A preconditioner is used to extend the method to low Mach and incompressible flows. We further extend the method to turbulent flows with the Spalart Allmaras model. We verify high-order accuracy via the method of manufactured solutions, method of exact solutions, and physical problems. Results obtained compare well to analytical solutions, numerical studies, and experimental data. It is foreseen that future application in the Naval field will be possible

Multi-Scale Models to Simulate Interactions between Liquid and Thin Structures

In this dissertation, we introduce a framework for simulating the dynamics between liquid and thin structures, including the effects of buoyancy, drag, capillary cohesion, dripping, and diffusion. After introducing related works, Part I begins with a discussion on the interactions between Newtonian fluid and fabrics. In this discussion, we treat both the fluid and the fabrics as continuum media; thus, the physical model is built from mixture theory. In Part II, we discuss the interactions between Newtonian fluid and hairs. To have more detailed dynamics, we no longer treat the hairs as continuum media. Instead, we treat them as discrete Kirchhoff rods. To deal with the thin layer of liquid that clings to the hairs, we augment each hair strand with a height field representation, through which we introduce a new reduced-dimensional flow model to solve the motion of liquid along the longitudinal direction of each hair. In addition, we develop a faithful model for the hairs' cohesion induced by surface tension, where a penalty force is applied to simulate the collision and cohesion between hairs. To enable the discrete strands interact with continuum-based, shear-dependent liquid, in Part III, we develop models that account for the volume change of the liquid as it passes through strands and the momentum exchange between the strands and the liquid. Accordingly, we extend the reduced-dimensional flow model to simulate liquid with elastoviscoplastic behavior. Furthermore, we use a constraint-based model to replace the penalty-force model to handle contact, which enables an accurate simulation of the frictional and adhesive effects between wet strands. We also present a principled method to preserve the total momentum of a strand and its surface flow, as well as an analytic plastic flow approach for Herschel-Bulkley fluid that enables stable semi-implicit integration at larger time steps. We demonstrate a wide range of effects, including the challenging animation scenarios involving splashing, wringing, and colliding of wet clothes, as well as flipping of hair, animals shaking, spinning roller brushes from car washes being dunked in water, and intricate hair coalescence effects. For complex liquids, we explore a series of challenging scenarios, including strands interacting with oil paint, mud, cream, melted chocolate, and pasta sauce

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

Verification and Validation of the Spalart-Allmaras Turbulence Model for Strand Grids

The strand-Cartesian grid approach is a unique method of generating and computing fluid dynamic simulations. The strand-Cartesian approach provides highly desirable qualities of fully-automatic grid generation and high-order accuracy. This thesis focuses on the implementation of the Spalart-Allmaras turbulence model to the strand-Cartesian grid framework. Verification and validation is required to ensure correct implementation of the turbulence model.Mathematical code verification is used to ensure correct implementation of new algorithms within the code framework. The Spalart-Allmaras model is verified with the Method of Manufactured Solutions (MMS). MMS shows second-order convergence, which implies that the new algorithms are correctly implemented.Validation of the strand-Cartesian solver is completed by simulating certain cases for comparison against the results of two independent compressible codes; CFL3D and FUN3D. The NASA-Langley turbulence resource provided the inputs and conditions required to run the cases, as well as the case results for these two codes. The strand solver showed excellent agreement with both NASA resource codes for a zero-pressure gradient flat plate and bump- in-channel. The treatment of the sharp corner on a NACA 0012 airfoil is investigated, resulting in an optimal external sharp corner configuration of strand vector smoothing with a base Cartesian grid and telescoping Cartesian refinement around the trailing edge. Results from the case agree well with those from CFL3D and FUN3D. Additionally, a NACA 4412 airfoil case is examined, and shows good agreement with CFL3D and FUN3D, resulting in validation for this case

Numerical modeling of the fiber deposition flow in extrusion-based 3D bioprinting

Extrusion bioprinting involves the deposition of bioinks in a layer-wise fashion to build 3D structures that mimic natural living systems\u27 behavior in tissue engineering. Hydrogels are the most common bioinks, in which their viscosity properties are dependent on the shear-rate, such as Non-Newtonian fluids. Numerical simulation of extrusion bioprinting may help study the flow properties of hydrogels and designing improved bioinks. In this thesis, the instability caused by the shear-thinning or -thickening parameter during extrusion is numerically compared with the theoretical estimations. The process of fiber deposition of hydrogels onto a substrate through the single and coaxial nozzle is done using a commercial package (ANSYS Fluent). For various power-law bioinks, the morphology of single and multi-layer 3D bioprinted fibers, including the velocity, printing pressure, wall shear stress, and mixing proportion of two bioinks during bioprinting, are predicted for the first time

Entropy Splitting and Numerical Dissipation

A rigorous stability estimate for arbitrary order of accuracy of spatial central difference schemes for initial boundary value problems of nonlinear symmetrizable systems of hyperbolic conservation laws was established recently by Olsson and Oliger (1994, “Energy and Maximum Norm Estimates for Nonlinear Conservation Laws,” RIACS Report, NASA Ames Research Center) and Olsson (1995, Math. Comput. 64, 212) and was applied to the two-dimensional compressible Euler equations for a perfect gas by Gerritsen and Olsson (1996, J. Comput. Phys. 129, 245) and Gerritsen (1996, “Designing an Efficient Solution Strategy for Fluid Flows, Ph.D. Thesis, Stanford). The basic building block in developing the stability estimate is a generalized energy approach based on a special splitting of the flux derivative via a convex entropy function and certain homogeneous properties. Due to some of the unique properties of the compressible Euler equations for a perfect gas, the splitting resulted in the sum of a conservative portion and a non-conservative portion of the flux derivative, hereafter referred to as the “entropy splitting.” There are several potentially desirable attributes and side benefits of the entropy splitting for the compressible Euler equations that were not fully explored in Gerritsen and Olsson. This paper has several objectives. The first is to investigate the choice of the arbitrary parameter that determines the amount of splitting and its dependence on the type of physics of current interest to computational fluid dynamics. The second is to investigate in what manner the splitting affects the nonlinear stability of the central schemes for long time integrations of unsteady flows such as in nonlinear aeroacoustics and turbulence dynamics. If numerical dissipation indeed is needed to stabilize the central scheme, can the splitting help minimize the numerical dissipation compared to its un-split cousin? Extensive numerical study on the vortex preservation capability of the splitting in conjunction with central schemes for long time integrations will be presented. The third is to study the effect of the non-conservative proportion of splitting in obtaining the correct shock location for high speed complex shock-turbulence interactions. The fourth is to determine if this method can be extended to other physical equations of state and other evolutionary equation sets. If numerical dissipation is needed, the Yee, Sandham, and Djomehri (1999, J. Comput. Phys. 150, 199) numerical dissipation is employed. The Yee et al. schemes fit in the Olsson and Oliger framework