Between Dec 19, 2024 and Jan 2, 2025, datasets can be submitted to DRUM but will not be processed until after the break. Staff will not be available to answer email during this period, and will not be able to provide DOIs until after Jan 2. If you are in need of a DOI during this period, consider Dryad or OpenICPSR. Submission responses to the UDC may also be delayed during this time.

Browsing by Subject "Numerical simulations"

Now showing 1 - 4 of 4
  • Thumbnail Image
    Item
    Numerical Simulations of Fluid-Structure Interaction Problems in Biological Flows
    (2008-06) Borazjani, Iman
    There has been increasing interest in the study of flows in biological systems in recent years. Examples range from blood flow in the cardiovascular systems to flows past swimming animals and organisms. Such flows take place in multi-connected domains with complex geometries, flexible moving boundaries, over a range of Reynolds numbers, and usually involve non-linear fluid/structure interactions (FSI). An efficient and versatile computational framework for simulating a wide range of biological flows with complex moving boundaries and FSI has been developed. This computational framework is based on the hybrid Cartesian/immersed boundary method of Gilmanov and Sotiropoulos [61] and the curvilinear/immersed boundary (CURVIB) method of Ge and Sotiropoulos [59]. This work has extended the above methods to non-linear FSI problems for multiple, arbitrarily complex bodies in a general non-inertial reference frame (CURVIB-FSI solver). The stability of the CURVIB-FSI computational framework for different FSI coupling methods has been analyzed by some simple, albeit similar, FSI problems and the behaviors of the FSI solver in the numerical experiments were explained. It was shown that the ratio of the added mass to the mass of the structure as well as the sign of the local time rate of change of the force or moment imparted on the structure by the fluid determine the stability and convergence of the FSI algorithm. The stabilizing role of under-relaxation is also clarified and the upper bound of the under-relaxation coefficient required for stability is derived. The CURVIB-FSI solver has been validated in both inertial and non-inertial reference frames by applying it to several well-studied FSI problem e.g. vortex-induced vibrations (VIV) of an elastically mounted cylinder. After demonstrating the accuracy and validity of the CURVIB-FSI, it is applied to simulate three important biological flows: 1) Flow through a bi-leaflet mechanical heart valves (BMHV); 2) Aquatic fishlike swimming; 3) Aquatic planktonic swimming. Each of these simulations is the most advanced in their field and pushes the limits of the state-of-the-art numerical simulations. Furthermore, new insights have been gained into the physics of these important flows, which with experiments alone would not have been possible.
  • Thumbnail Image
    Item
    Numerical Simulations of the Two-phase flow and Fluid-Structure Interaction Problems with Adaptive Mesh Refinement
    (2022-03) Zeng, Yadong
    Numerical simulations of two-phase flow and fluid structure interaction problems are of great interest in many environmental problems and engineering applications. To capture the complex physical processes involved in these problems, a high grid resolution is usually needed. However, one does not need or maybe cannot afford a fine grid of uniformly high resolution across the whole domain. The need to resolve local fine features can be addressed by the adaptive mesh refinement (AMR) method, which increases the grid resolution in regions of interest as needed during the simulation while leaving general estimates in other regions. In this work, we propose a block-structured adaptive mesh refinement (BSAMR) framework to simulate two-phase flows using the level set (LS) function with both the subcycling and non-subcycling methods on a collocated grid. To the best of our knowledge, this is the first framework that unifies the subcycling and non-subcycling methods to simulate two-phase flows. The use of the collocated grid is also the first among the two-phase BSAMR framework, which significantly simplifies the implementation of multi-level differential operators and interpolation schemes. We design the synchronization operations, including the averaging, refluxing, and synchronization projection, which ensures that the flow field is divergence-free on the multi-level grid. It is shown that the present multi-level scheme can accurately resolve the interfaces of the two-phase flows with gravitational and surface tension effects while having good momentum and energy conservation. We then develop another consistent scheme, in which the conservative momentum equations and the mass equation are solved in the aforementioned BSAMR framework. This consistent mass and momentum transport treatment greatly improves the accuracy and robustness for simulating two-phase flows with a high density ratio and high Reynolds number. We demonstrate that the consistent scheme results in a numerically stable solution in flows with high density ratios~(up to $10^6$) and high Reynolds numbers~(up to $10^6$), while the inconsistent scheme exhibits nonphysical fluid behaviors in these tests. For solving single- and multiphase fluid-structure interaction (FSI) problems, we present an adaptive implementation of the distributed Lagrange multiplier (DLM) immersed boundary (IB) method on multilevel collocated grids. We also developed a force-averaging algorithm to maintain the consistency of Eulerian immersed boundary (IB) forces across multiple levels. The efficacy of the force averaging algorithm is validated using the lid-driven cavity with a submerged cylinder problem. We demonstrate the versatility of the present multilevel framework by simulating problems with various types of kinematic constraints imposed by structures on fluids, such as imposing a prescribed motion, free motion, and time-evolving shape of a solid body. The accuracy and robustness of the codes are validated using several canonical test problems.
  • Thumbnail Image
    Item
    On some PDF based moment closure approximations of micro-macro models for viscoelastic polymeric fluids
    (University of Minnesota. Institute for Mathematics and Its Applications, 2009-01) Hyon, Yunkyong; Du, Qiang; Liu, Chun
  • Thumbnail Image
    Item
    Three-dimensional boundary element analysis of fractured rock
    (2016-03) Nikolskiy, Dmitry
    Understanding the mechanisms of rock fracture is of key importance to the mining and petroleum industries. Rock masses feature complicated geometry and structure including joints, heterogeneities of different scales (e.g. grains, pores, macroscopic inhomogeneities, etc.) and may be subject to various effects of injected fluid pressure, temperature gradient, etc. Therefore, comprehensive three-dimensional computational models that would allow to adequately treat complex behavior of a rock mass are required. Among the industrial applications of such models are the quantification of safety of underground workings and simulation of hydraulic fracturing. The dissertation presents a new Boundary Element Method-based technique for analysis of a three-dimensional elastic medium containing multiple cracks and/or openings of arbitrary shapes. The technique employs planar triangular elements to discretize the boundaries and quadratic polynomials to approximate the boundary unknowns, with two options of the arrangement of the nodal points on the elements. The novel features of the technique include the following: • the use of complex variable formalism involving various combinations of the geometrical parameters and the elastic fields, e.g. components of tractions and displacement discontinuities in the plane of the considered element; • analytical integration with the use of Cauchy-Pompeiu formula to reduce the surface integrals to the contour ones; • “limit after integration" approach, i.e. enforcing the boundary conditions after the discretization and analytical handling of the internal fields, by allowing the field point to reach the boundaries. The method can still capture the behavior of stress field near the crack fronts (tips) although no special approximating functions (tip asypmtotics) are used. The solutions of some benchmark problems are provided to demonstrate the capabilities of the proposed method.