Modeling Environmental Flows at a Range of Scales Using Adaptive Methods 
(Matt Piggott, Imperial College UK) 
The concept is to allocate computational resources to nodes where most needed 
to optimize computing costs in the simulation of nonhydrostatic dynamics, using
the freedom to choose the sub-grid scale (SGS) to our advantage while
maintaining due regard for how variable resolution and differential
discretization modelling options interact.  Given that variable
resolution via mesh adaptivity and stabilized discretization methods
typically introduce some kind of dissipation, there is need for an
underlying numerical method that does not introduce grid scale noise
and minimizes spurious dispersion or dissipation.  The main aim is to
develop a new modelling framework able to simultaneously resolve
coupled dynamics at a range of scales while removing spurious noise
in geophysical scale applications.  Mesh optimization makes local
topological changes to the mesh so that it appears homogeneous and
isotropic in the transformed space defined by an error metric tensor.
 Unstructured meshes represent an excellent framework for anisotropic
mesh adaptivity.  Other advantages include: accurate efficient domain
representation, imposition of boundary conditions, and mesh
flexibility in all directions.  The mesh optimization procedure, to
amend differential equations via an operator and perform a Galerkin
discretization, leads to a variety of stabilized numerical methods. 
The Galerkin Least Squares SGS method is the simplest proposed
variational multiscale method, which was utilized to achieve a
third-order accurate scheme with a leading order fourth-order
dissipation term.  The sensitivity/adjoint goal based error measures
were constructed from the solution of an adjoint problem and the
model residual (estimates of which should contain contributions due
to both discretization and modelling).  

Summary:
Unstructured adaptive mesh methods are able to robustly solve for
environmental and geophysical flows; Numerical method needs to
minimize spurious dissipation so that there is no “double-counting”
when SGS modelling is employed; Error measure can have contributions
from discretization errors, turbulence models, and in principle
models of other SGS physics; Possibility exists to test SGS models of
certain processes by simply resolving them in a calculation; A
high-order implicit numerical stabilization (ILES) is currently in
implementation; Main question- Does the mesh adaptivity inhibit any
true physical behaviour (e.g. vertical mixing/convective plumes), and
to what extent are results model independent?