scholarly journals Accounting for Nonlinear Aspects in Multiphysics Problems: Application to Poroelasticity

2004 ◽  
pp. 612-620
Author(s):  
David Néron ◽  
Pierre Ladevèze ◽  
David Dureisseix ◽  
Bernard A. Schrefler
Keyword(s):  
Multiphysics Problems

Model of induction brazing of nonmagnetic metals using model order reduction approach

2018 ◽  
Vol 37 (4) ◽  
pp. 1515-1524 ◽  
Author(s):  
Pavel Karban ◽  
David Pánek ◽  
Ivo Doležel
Keyword(s):  
Heat Treatment ◽  
Model Order Reduction ◽  
Computation Time ◽  
Order Reduction ◽  
Nonlinear Problems ◽  
Model Order ◽  
Content Type ◽  
Weakly Nonlinear ◽  
Induction Brazing ◽  
Multiphysics Problems

Purpose A novel technique for control of complex physical processes based on the solution of their sufficiently accurate models is presented. The technique works with the model order reduction (MOR), which significantly accelerates the solution at a still acceptable uncertainty. Its advantages are illustrated with an example of induction brazing. Design/methodology/approach The complete mathematical model of the above heat treatment process is presented. Considering all relevant nonlinearities, the numerical model is reduced using the orthogonal decomposition and solved by the finite element method (FEM). It is cheap compared with classical FEM. Findings The proposed technique is applicable in a wide variety of linear and weakly nonlinear problems and exhibits a good degree of robustness and reliability. Research limitations/implications The quality of obtained results strongly depends on the temperature dependencies of material properties and degree of nonlinearities involved. In case of multiphysics problems characterized by low nonlinearities, the results of solved problems differ only negligibly from those solved on the full model, but the computation time is lower by two and more orders. Yet, however, application of the technique in problems with stronger nonlinearities was not fully evaluated. Practical implications The presented model and methodology of its solution may represent a basis for design of complex technologies connected with induction-based heat treatment of metal materials. Originality/value Proposal of a sophisticated methodology for solution of complex multiphysics problems established the MOR technology that significantly accelerates their solution at still acceptable errors.

scholarly journals Coupling Requirements for Multiphysics Problems Posed on Two Domains

2017 ◽  
Vol 55 (6) ◽  
pp. 2885-2904 ◽  
Author(s):  
Fatemeh Ghasemi ◽  
Jan Nordström
Keyword(s):  
Multiphysics Problems

Combining Imaging Modalities in the Modeling of Multiparameter Devices

2013 ◽  
Vol 7 (4) ◽  
Author(s):  
Jens Vinge Nygaard
Keyword(s):  
Numerical Analysis ◽  
Fluid Mechanics ◽  
Modeling And Simulation ◽  
Medical Devices ◽  
Numerical Models ◽  
Imaging Modalities ◽  
Length Scales ◽  
Geometrical Information ◽  
Multiphysics Problems

Modeling and simulation of medical devices are typically established to identify parameter dependencies within the system of interest. Most devices are multiphysics problems considering solid and fluid mechanics, and electromagnetic mechanisms bridging time and length scales. Typically, the geometries of interest are described by complex morphologies of biological components. These factors all contribute to significant complexity of the developed numerical models. Access to imaging modalities capable of providing the geometrical information of relevance is central in the establishment and verification of numerical analysis. Here, data from image-based models obtained with MRI and μCT to risk access patients prone to realizing stroke, and to evaluate drug eluding scaffolds is presented.

scholarly journals PorePy: an open-source software for simulation of multiphysics processes in fractured porous media

2020 ◽  
Author(s):  
Eirik Keilegavlen ◽  
Runar Berge ◽  
Alessio Fumagalli ◽  
Michele Starnoni ◽  
Ivar Stefansson ◽  
...  
Keyword(s):  
Porous Media ◽  
Open Source ◽  
Open Source Software ◽  
Fractured Rocks ◽  
Fractured Reservoirs ◽  
Simulation Software ◽  
Coupled Processes ◽  
Fracture Networks ◽  
Flow And Transport ◽  
Multiphysics Problems

Abstract Development of models and dedicated numerical methods for dynamics in fractured rocks is an active research field, with research moving towards increasingly advanced process couplings and complex fracture networks. The inclusion of coupled processes in simulation models is challenged by the high aspect ratio of the fractures, the complex geometry of fracture networks, and the crucial impact of processes that completely change characteristics on the fracture-rock interface. This paper provides a general discussion of design principles for introducing fractures in simulators, and defines a framework for integrated modeling, discretization, and computer implementation. The framework is implemented in the open-source simulation software PorePy, which can serve as a flexible prototyping tool for multiphysics problems in fractured rocks. Based on a representation of the fractures and their intersections as lower-dimensional objects, we discuss data structures for mixed-dimensional grids, formulation of multiphysics problems, and discretizations that utilize existing software. We further present a Python implementation of these concepts in the PorePy open-source software tool, which is aimed at coupled simulation of flow and transport in three-dimensional fractured reservoirs as well as deformation of fractures and the reservoir in general. We present validation by benchmarks for flow, poroelasticity, and fracture deformation in porous media. The flexibility of the framework is then illustrated by simulations of non-linearly coupled flow and transport and of injection-driven deformation of fractures. All results can be reproduced by openly available simulation scripts.

scholarly journals Embedded Zassenhaus Expansion to Splitting Schemes: Theory and Multiphysics Applications

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Jürgen Geiser
Keyword(s):  
Fluid Dynamics ◽  
Convergence Rates ◽  
Operator Splitting ◽  
Main Idea ◽  
Computation Time ◽  
Product Formula ◽  
Splitting Methods ◽  
Splitting Schemes ◽  
Operator Splitting Methods ◽  
Multiphysics Problems

We present some operator splitting methods improved by the use of the Zassenhaus product and designed for applications to multiphysics problems. We treat iterative splitting methods that can be improved by means of the Zassenhaus product formula, which is a sequential splitting scheme. The main idea for reducing the computation time needed by the iterative scheme is to embed fast and cheap Zassenhaus product schemes, since the computation of the commutators involved is very cheap, since we are dealing with nilpotent matrices. We discuss the coupling ideas of iterative and sequential splitting techniques and their convergence. While the iterative splitting schemes converge slowly in their first iterative steps, we improve the initial convergence rates by embedding the Zassenhaus product formula. The applications are to multiphysics problems in fluid dynamics. We consider phase models in computational fluid dynamics and analyse how to obtain higher order operator splitting methods based on the Zassenhaus product. The computational benefits derive from the use of sparse matrices, which arise from the spatial discretisation of the underlying partial differential equations. Since the Zassenhaus formula requires nearly constant CPU time due to its sparse commutators, we have accelerated the iterative splitting schemes.

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