237 research outputs found
Spectral/hp element methods: recent developments, applications, and perspectives
The spectral/hp element method combines the geometric flexibility of the
classical h-type finite element technique with the desirable numerical
properties of spectral methods, employing high-degree piecewise polynomial
basis functions on coarse finite element-type meshes. The spatial approximation
is based upon orthogonal polynomials, such as Legendre or Chebychev
polynomials, modified to accommodate C0-continuous expansions. Computationally
and theoretically, by increasing the polynomial order p, high-precision
solutions and fast convergence can be obtained and, in particular, under
certain regularity assumptions an exponential reduction in approximation error
between numerical and exact solutions can be achieved. This method has now been
applied in many simulation studies of both fundamental and practical
engineering flows. This paper briefly describes the formulation of the
spectral/hp element method and provides an overview of its application to
computational fluid dynamics. In particular, it focuses on the use the
spectral/hp element method in transitional flows and ocean engineering.
Finally, some of the major challenges to be overcome in order to use the
spectral/hp element method in more complex science and engineering applications
are discussed
SPH modeling and simulation of spherical particles interacting in a viscoelastic matrix
In this work, we extend the three-dimensional Smoothed Particle Hydrodynamics (SPH) non-colloidal particulate model previously developed for Newtonian suspending media in Vázquez-Quesada and Ellero [“Rheology and microstructure of non-colloidal suspensions under shear studied with smoothed particle hydrodynamics,” J. Non-Newtonian Fluid Mech. 233, 37–47 (2016)] to viscoelastic matrices. For the solvent medium, the coarse-grained SPH viscoelastic formulation proposed in Vázquez-Quesada, Ellero, and Español [“Smoothed particle hydrodynamic model for viscoelastic fluids with thermal fluctuations,” Phys. Rev. E 79, 056707 (2009)] is adopted. The property of this particular set of equations is that they are entirely derived within the general equation for non-equilibrium reversible-irreversible coupling formalism and therefore enjoy automatically thermodynamic consistency. The viscoelastic model is derived through a physical specification of a conformation-tensor-dependent entropy function for the fluid particles. In the simple case of suspended Hookean dumbbells, this delivers a specific SPH discretization of the Oldroyd-B constitutive equation. We validate the suspended particle model by studying the dynamics of single and mutually interacting “noncolloidal” rigid spheres under shear flow and in the presence of confinement. Numerical results agree well with available numerical and experimental data. It is straightforward to extend the particulate model to Brownian conditions and to more complex viscoelastic solvents
An Immersed Interface Method for Discrete Surfaces
Fluid-structure systems occur in a range of scientific and engineering
applications. The immersed boundary(IB) method is a widely recognized and
effective modeling paradigm for simulating fluid-structure interaction(FSI) in
such systems, but a difficulty of the IB formulation is that the pressure and
viscous stress are generally discontinuous at the interface. The conventional
IB method regularizes these discontinuities, which typically yields low-order
accuracy at these interfaces. The immersed interface method(IIM) is an IB-like
approach to FSI that sharply imposes stress jump conditions, enabling
higher-order accuracy, but prior applications of the IIM have been largely
restricted to methods that rely on smooth representations of the interface
geometry. This paper introduces an IIM that uses only a C0 representation of
the interface,such as those provided by standard nodal Lagrangian FE methods.
Verification examples for models with prescribed motion demonstrate that the
method sharply resolves stress discontinuities along the IB while avoiding the
need for analytic information of the interface geometry. We demonstrate that
only the lowest-order jump conditions for the pressure and velocity gradient
are required to realize global 2nd-order accuracy. Specifically,we show
2nd-order global convergence rate along with nearly 2nd-order local convergence
in the Eulerian velocity, and between 1st-and 2nd-order global convergence
rates along with 1st-order local convergence for the Eulerian pressure. We also
show 2nd-order local convergence in the interfacial displacement and velocity
along with 1st-order local convergence in the fluid traction. As a
demonstration of the method's ability to tackle complex geometries,this
approach is also used to simulate flow in an anatomical model of the inferior
vena cava.Comment: - Added a non-axisymmetric example (flow within eccentric rotating
cylinder in Sec. 4.3) - Added a more in-depth analysis and comparison with a
body-fitted approach for the application in Sec. 4.
Advances in Time-Domain Electromagnetic Simulation Capabilities Through the Use of Overset Grids and Massively Parallel Computing
A new methodology is presented for conducting numerical simulations of electromagnetic scattering and wave propagation phenomena. Technologies from several scientific disciplines, including computational fluid dynamics, computational electromagnetics, and parallel computing, are uniquely combined to form a simulation capability that is both versatile and practical. In the process of creating this capability, work is accomplished to conduct the first study designed to quantify the effects of domain decomposition on the performance of a class of explicit hyperbolic partial differential equations solvers; to develop a new method of partitioning computational domains comprised of overset grids; and to provide the first detailed assessment of the applicability of overset grids to the field of computational electromagnetics. Furthermore, the first Finite Volume Time Domain (FVTD) algorithm capable of utilizing overset grids on massively parallel computing platforms is developed and implemented. Results are presented for a number of scattering and wave propagation simulations conducted using this algorithm, including two spheres in close proximity and a finned missile
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