## Applied and Computational Mathematics Seminars 2011 - 2012

### Programme

These seminars take place on Tuesdays, in Room M/2.06, Senghennydd Road, Cardiff from 3pm, unless otherwise stated.

When a seminar is not scheduled there is a collaborative workshop with other groups within the College of Physical Sciences & Engineering or a SIAM Chapter Meeting. Further details can be found on the School Diary.

##### 18 October 2011

**Speaker:** Steve Lind (Manchester Metropolitan).

**Title:** Incompressible SPH.

**Abstract:** TBC.

##### 20 October 2011 at 2pm in Room M/1.25

**Speaker:** David Leppinen (Birmingham).

**Title:** The interaction of cavitation bubbles with a density interface.

**Abstract:** TBC.

##### 22 November 2011

**Speaker:** Tim Reis (Oxford).

**Title:** Lattice Boltzmann equations for multiphase flows.

**Abstract:** TBC.

##### 29 November 2011

**Speaker:** Apala Majumdar (Oxford).

**Title:** Liquid Crystals - Modelling and Applications.

**Abstract:** TBC.

##### 6 December 2011

**Speaker:** Erik Burman (Sussex).

**Title:** Nitsche type unfitted FEM in fictitious domain methods and XFEM.

**Abstract:** TBC.

##### 16 January 2012 at 14:00 in Room M/2.06

**Speaker:** Davide Deganello (Swansea).

**Title:** Printing of functional fluids: technologies, modelling & challenges.

**Abstract:** TBC.

##### 7 February 2012 at 16:00 in Room M/2.06

**Speaker:** Sven Gross (Aachen).

**Title:**3D incompressible two-phase flow simulations with XFEM.

**Abstract:** TBC.

##### 21 February 2012

**Speaker:** Penny Davies (Strathclyde).

**Title:** Convolution quadrature revisited for integral and boundary integral equations.

**Abstract:** Convolution quadrature (CQ) methods were introduced by Lubich in 1988 to
approximate convolution integrals. More recently they have been used
for the temporal approximation of time--dependent boundary integral

equations together with a finite element or collocation approximation in
space, because they typically give a more stable numerical algorithm
than standard time-stepping methods. The drawback is that the support
of the associated CQ basis functions is infinite, which gives rise to
dense system matrices and makes the method inefficient. I shall
describe some recent work (with Dugald Duncan) which shows how using a
spline-based implementation of the CQ methodology can circumvent this.

##### 28 February 2012

**Speaker:** Olivier Goury (ENGIN).

**Title: **Algebraic coarse-graining methods in fracture mechanics: tackling local lack of correlation using domain decomposition.

**Abstract:** TBC.

##### 06 March 2012

**Speaker:** Robert Owens (Montreal).

**Title: **A New Incompressible Smoothed Particle Hydrodynamics-Immersed Boundary Method

**Abstract:** In this talk we develop a new smoothed particle hydrodynamics (SPH) method
suitable for solving the
incompressible Navier-Stokes equations, even with singular forces.
Singular source terms are handled
in a manner similar to that in the immersed boundary (IB) method of Peskin
(2002). The numerical scheme
implements a second-order pressure-free projection method due to Kim and
Moin (1985) and completely
obviates the difficulties that may be faced in prescribing Neumann
pressure boundary conditions. The proposed
SPH method is first tested on the planar start-up Poiseuille problem and a
detailed error analysis is performed. For this problem, the results are
similar whether the SPH particles are free to move or fixed on a regular
grid. Our hybrid SPH-IB method is then used to calculate the dynamics of a
stretched immersed elastic membrane and the advantages in this case of
fixing the SPH particles, rather than allowing them to move with the
fluid, are discussed.

##### 20 March 2012

**Speaker:** Anatoly Zhigljavsky (MATHS, Cardiff).

**Title: **Fast iteration methods for solving linear equations.

**Abstract:** TBC.

##### 20 March 2012

**Speaker:** Fehmi Cirak (Cambridge).

**Title: **Subdivision-stabilised Immersed B-Spline Finite Elements for Fluid-Structure Interaction.

**Abstract:** TBC.

##### 1 May 2012

**Speaker:** Peter Bollada (Leeds).

**Title: **Continuum modelling of crystal formation: "Metal-flakes".

**Abstract:** Modelling of crystal formation is done using the tools of

non-equilibrium thermodynamics combined with knowledge of the

equilibrium thermodynamics of matter- principally its free energy. In

its equilibrium state the free energy of the material is at its minimum.

Metals can be cooled just below their freezing point and yet remain in

their liquid phase (undercooled liquid). This may be explained by noting

that the free energy has two equilibrium states at this temperature: one

liquid and one solid. If a growing surface, typically a particle of

dust, is introduced into the undercooled liquid a solid crystal forms

very rapidly. The modeling of this phenomena in a pure metal requires

only two variables: Temperature and Phase, where the phase variable

typically has value zero for liquid and unity for solid. The interface

between the two states of matter is conveniently spread to make the

resulting coupled PDEs computationally tractable.

##### 15 May 2012

**Speaker:** Oliver Jensen (Nottingham).

**Title: ** Multiscale models of growth and transport in biological tissues .

**Abstract: **In building mathematical models of biological tissues, it is often necessary to link phenomena operating at very disparate lengthscales. I will describe two applications, each with a biomechanical flavour, where we have used multiscale approaches to relate microscopic and macroscopic processes. The first is a growing plant root, where a hierarchy of models are needed to connect the action of hormones and enzymes on the walls of individual plant cells to the development of the whole organ. The second example is the human placenta, where maternal blood flows past a disordered array of fetal blood vessels; here we investigate the usefulness ofhomogenization approximations in stochastic domains.