
A Reduced Order Cut Finite Element method for geometrically parameterized steady and unsteady NavierStokes problems
This work focuses on steady and unsteady NavierStokes equations in a re...
read it

A ReducedOrder Shifted Boundary Method for Parametrized incompressible NavierStokes equations
We investigate a projectionbased reducedorder model of the steady inco...
read it

Nonintrusive PODIROM for patientspecific aortic blood flow in presence of a LVAD device
Left ventricular assist devices (LVADs) are used to provide haemodynamic...
read it

Immersed boundary finite element method for blood flow simulation
We present an efficient and accurate immersed boundary (IB) finite eleme...
read it

A geometric multigrid method for spacetime finite element discretizations of the NavierStokes equations and its application to 3d flow simulation
We present a parallelized geometric multigrid (GMG) method, based on the...
read it

Multipreconditioning with application to twophase incompressible NavierStokes flow
We consider the use of multipreconditioning to solve linear systems when...
read it

Nonintrusive proper generalised decomposition for parametrised incompressible flow problems in OpenFOAM
The computational cost of parametric studies currently represents the ma...
read it
Model order reduction of flow based on a modular geometrical approximation of blood vessels
We are interested in a reduced order method for the efficient simulation of blood flow in arteries. The blood dynamics is modeled by means of the incompressible NavierStokes equations. Our algorithm is based on an approximated domaindecomposition of the target geometry into a number of subdomains obtained from the parametrized deformation of geometrical building blocks (e.g. straight tubes and model bifurcations). On each of these building blocks, we build a set of spectral functions by proper orthogonal decomposition of a large number of snapshots of finite element solutions (offline phase). The global solution of the NavierStokes equations on a target geometry is then found by coupling linear combinations of these local basis functions by means of spectral Lagrange multipliers (online phase). Being that the number of reduced degrees of freedom is considerably smaller than their finite element counterpart, this approach allows us to significantly decrease the size of the linear system to be solved in each iteration of the NewtonRaphson algorithm. We achieve large speedups with respect to the full order simulation (in our numerical experiments, the gain is at least of one order of magnitude and grows inversely with respect to the reduced basis size), whilst still retaining satisfactory accuracy for most cardiovascular simulations.
READ FULL TEXT
Comments
There are no comments yet.