328 research outputs found
Results towards a Scalable Multiphase Navier-Stokes Solver for High Reynolds Number Flows
The incompressible Navier-Stokes equations have proven formidable for nearly a century. The present difficulties are mathematical and computational in nature; the computational requirements, in particular, are exponentially exacerbated in the presence of high Reynolds number. The issues are further compounded with the introduction of markers or an immiscible fluid intended to be tracked in an ambient high Reynolds number flow; despite the overwhelming pragmatism of problems in this regime, and increasing computational efficacy, even modest problems remain outside the realm of direct approaches.
Herein three approaches are presented which embody direct application to problems of this nature. An LES model based on an entropy-viscosity serves to abet the computational resolution requirements imposed by high Reynolds numbers and a one-stage compressive flux, also utilizing an entropy-viscosity, aids in accurate, efficient, conservative transport, free of low order dispersive error, of an immiscible fluid or tracer. Finally, an integral commutator and the theory of anti-dispersive spaces is introduced as a novel theoretical tool for consistency error analysis; in addition the material engenders the construction of error-correction techniques for mass lumping schemes
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Geometric Numerical Integration
The subject of this workshop was numerical methods that preserve geometric properties of the flow of an ordinary or partial differential equation. This was complemented by the question as to how structure preservation affects the long-time behaviour of numerical methods
A convergent evolving finite element algorithm for Willmore flow of closed surfaces
A proof of convergence is given for a novel evolving surface finite element
semi-discretization of Willmore flow of closed two-dimensional surfaces, and
also of surface diffusion flow. The numerical method proposed and studied here
discretizes fourth-order evolution equations for the normal vector and mean
curvature, reformulated as a system of second-order equations, and uses these
evolving geometric quantities in the velocity law interpolated to the finite
element space. This numerical method admits a convergence analysis in the case
of continuous finite elements of polynomial degree at least two. The error
analysis combines stability estimates and consistency estimates to yield
optimal-order -norm error bounds for the computed surface position,
velocity, normal vector and mean curvature. The stability analysis is based on
the matrix--vector formulation of the finite element method and does not use
geometric arguments. The geometry enters only into the consistency estimates.
Numerical experiments illustrate and complement the theoretical results
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Surface, Bulk, and Geometric Partial Differential Equations: Interfacial, stochastic, non-local and discrete structures
Partial differential equations in complex domains with free\linebreak boundaries
and interfaces continue to be flourishing research areas at the
interfaces between PDE theory, differential geometry, numerical
analysis and applications.
Main themes of the workshop have been PDEs on evolving domains, phase
field approaches, interactions of bulk and surface PDEs, curvature
driven evolution equations. Applications particular from biology, such
as cell and cancer modelling and fluid as well solid mechanics have been
subjects of the conference
Self-Evaluation Applied Mathematics 2003-2008 University of Twente
This report contains the self-study for the research assessment of the Department of Applied Mathematics (AM) of the Faculty of Electrical Engineering, Mathematics and Computer Science (EEMCS) at the University of Twente (UT). The report provides the information for the Research Assessment Committee for Applied Mathematics, dealing with mathematical sciences at the three universities of technology in the Netherlands. It describes the state of affairs pertaining to the period 1 January 2003 to 31 December 2008
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Nonlinear Data: Theory and Algorithms
Techniques and concepts from differential geometry are used in many parts of applied mathematics today. However, there is no joint community for users of such techniques. The workshop on Nonlinear Data assembled researchers from fields like numerical linear algebra, partial differential equations, and data analysis to explore differential geometry techniques, share knowledge, and learn about new ideas and applications
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