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The model order reduction methodology of reduced basis (RB)
techniques offers efficient treatment of parametrized partial differential
equations (P2DEs) by providing both approximate solution procedures and
efficient error estimates.
RB-methods have so far mainly been applied to finite element schemes
for elliptic and parabolic problems. In the current study
we extend the methodology to general linear evolution schemes such as finite volume schemes for parabolic and hyperbolic evolution equations....
This paper is concerned with the numerical approximation of the solutions of a two-fluid two-pressure model used in the modelling of two-phase flows.
We present a relaxation strategy for easily dealing with both the
nonlinearities associated with the pressure laws and the nonconservative terms
that are inherently present in the set of convective equations and that couple the two phases.
In particular, the proposed approximate Riemann solver is given by explicit formulas, preserves
the natural...
In this work, we propose a general framework for the construction of pressure law for phase transition. These equations of state are particularly suitable for a use in a relaxation finite volume scheme. The approach is based on a constrained convex optimization
problem on the mixture entropy. It is valid for both miscible and immiscible mixtures. We also propose a rough pressure law for modelling a super-critical fluid.
We show that it is possible to construct a class of entropic schemes for the multicomponent Euler system describing a gas or fluid homogeneous mixture at thermodynamic equilibrium by applying a relaxation technique. A first order Chapman–Enskog expansion shows that the relaxed system formally converges when the relaxation frequencies go to the infinity toward a multicomponent Navier–Stokes system with the classical Fick and Newton laws, with a thermal diffusion which can be assimilated to a Soret...
We show that it is possible to construct a class of entropic
schemes for the multicomponent Euler system describing a gas or fluid
homogeneous mixture at thermodynamic equilibrium by applying a relaxation technique. A
first order Chapman–Enskog expansion shows that the relaxed system
formally converges when the relaxation frequencies go to the infinity
toward a multicomponent Navier–Stokes system with the classical Fick and
Newton laws, with a thermal diffusion which can be assimilated to a Soret...
We analyze residual and hierarchical a posteriori error estimates for nonconforming finite element approximations of elliptic problems with variable coefficients. We consider a finite volume box scheme equivalent to a nonconforming mixed finite element method in a Petrov–Galerkin setting. We prove that all the estimators yield global upper and local lower bounds for the discretization error. Finally, we present results illustrating the efficiency of the estimators, for instance, in the simulation...
We analyze residual and hierarchical
a posteriori error estimates for nonconforming finite element
approximations of elliptic problems with variable coefficients.
We consider a finite volume box scheme equivalent to
a nonconforming mixed finite element method in a Petrov–Galerkin
setting. We prove that
all the estimators yield global upper and local lower bounds for the discretization
error. Finally, we present results illustrating the efficiency of the
estimators, for instance, in the simulation...
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