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In this paper we outline the hyperbolic system of governing equations describing one-dimensional blood flow in arterial networks. This system is numerically discretised using a discontinuous Galerkin formulation with a spectral/ element spatial approximation. We apply the numerical model to arterial networks in the placenta. Starting with a single placenta we investigate the velocity waveform in the umbilical artery and its relationship with the distal bifurcation geometry and the terminal resistance....
In this paper we outline the hyperbolic system of governing equations
describing one-dimensional blood flow in arterial networks. This
system is numerically discretised using a discontinuous Galerkin
formulation with a spectral/hp element spatial approximation. We
apply the numerical model to arterial networks in the
placenta. Starting with a single placenta we investigate the velocity waveform
in the umbilical artery and its relationship with the distal
bifurcation geometry and the terminal resistance....
We semi-discretize in space a time-dependent Navier-Stokes system on a three-dimensional polyhedron by finite-elements schemes defined on two grids. In the first step, the fully non-linear problem is semi-discretized on a coarse grid, with mesh-size . In the second step, the problem is linearized by substituting into the non-linear term, the velocity computed at step one, and the linearized problem is semi-discretized on a fine grid with mesh-size . This approach is motivated by the fact that,...
We semi-discretize in space a time-dependent Navier-Stokes system
on a three-dimensional polyhedron by finite-elements schemes
defined on two grids. In the first step, the fully non-linear
problem is semi-discretized on a coarse grid, with mesh-size H.
In the second step, the problem is linearized by substituting
into the non-linear term, the velocity uH computed at step
one, and the linearized problem is semi-discretized on a fine
grid with mesh-size h. This approach is motivated by the fact
that,...
In this article, we present a new two-level stabilized nonconforming finite elements method for the two dimensional Stokes problem. This method is based on a local Gauss integration technique and the mixed nonconforming finite element of the pair (nonconforming linear element for the velocity, conforming linear element for the pressure). The two-level stabilized finite element method involves solving a small stabilized Stokes problem on a coarse mesh with mesh size and a large stabilized Stokes...
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