Adaptive modeling and numerical approximation for a simple example of multiscale hyperbolic relaxation system
Visualitza/Obre
Estadístiques de LA Referencia / Recolecta
Inclou dades d'ús des de 2022
Cita com:
hdl:2117/333797
Tipus de documentText en actes de congrés
Data publicació2015
EditorCIMNE
Condicions d'accésAccés obert
Tots els drets reservats. Aquesta obra està protegida pels drets de propietat intel·lectual i
industrial corresponents. Sense perjudici de les exempcions legals existents, queda prohibida la seva
reproducció, distribució, comunicació pública o transformació sense l'autorització del titular dels drets
Abstract
The present work considers the mathematical and numerical analysis of a new adaptive goal-oriented strategy
based on local hpm discontinuous Galerkin (DG) method (h for grid, p for accuracy of shape function and m for
model). In order to perform an exhaustive analysis, we consider steady-state solutions to the one-dimensional
linear hyperbolic system with multiple relaxation times ε ( x ) :
∂t uε+∂x vε = 0, x ∈[ 0,L ] , t >0,
∂t v ε +a2 ∂x uε = −1/ε ( x ) (v ε−buε ) ,
(1)
with L> 0 , a , b given constants satisfying 0<∣b∣< a and prescribed initial and boundary conditions [1].
The above system, for which the associated equilibrium equation reads ∂t u+ ∂x bu= 0, t > 0 (2), may be
viewed as a simple model of a hierarchy of PDE systems arranged according to a cascade of relaxation
mechanisms. For instance, such relaxation systems are involved in the study of multiphase flows or multiscale
coupling problems. In regions where ε is small, the numerical approximation of the full system (1) may
become very costly and a strategy to overcome this difficulty may consist in approximating the associated
steady-state equilibrium equation.
According to the main features of the flow and to the required accuracy of the description, the model, coarse
(2) or fine (1), has to be locally adapted for computational efficiency. Then, these different models have to be
appropriately coupled at some interfaces [2]. The automatic choice of the appropriate model requires model
adaptation procedures [3] where the position of the interface has to be optimized in such a way that in the
region where one computes the coarse model, the model error (expressed in term of output functionals)
between the fine and coarse models does not exceed some given tolerance. Nevertheless, only an
approximation of the adapted model is known in practice, thus the approximation involves both a model and a
discretization error [4]. These two kinds of errors have to be localized for the model and numerical adaptation
procedure.
The main goal of this work is to understand how the error of our hpm DG method depends on the relaxation
parameter, the boundary layer effects and the coupling interface layer effects in order to validate our approach.
Special emphasis is given to the theoretical (PDE level) study of the modeling error. Numerical experiments
will be considered to assess the performances of the present method.
CitacióCoquel, F. [et al.]. Adaptive modeling and numerical approximation for a simple example of multiscale hyperbolic relaxation system. A: ADMOS 2015. CIMNE, 2015, p. 54.
Fitxers | Descripció | Mida | Format | Visualitza |
---|---|---|---|---|
Admos2015-33-ADAPTIVE MODELING AND NUMERICAL.pdf | 154,2Kb | Visualitza/Obre |