Discretization and Parallel Iterative Schemes for Advection-Diffusion-Reaction Problems

Date

2015-09-18

Author

Sivas, Abdullah Ali
Manguoğlu, Murat
Boonkkamp, J. H. M. ten Thije
Anthonissen, M. J. H.

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

54
views

0
downloads

Conservation laws of advection-diffusion-reaction (ADR) type are ubiquitous in continuum physics. In this paper we outline discretization of these problems and iterative schemes for the resulting linear system. For discretization we use the finite volume method in combination with the complete flux scheme. The numerical flux is the superposition of a homogeneous flux, corresponding to the advection-diffusion operator, and the inhomogeneous flux, taking into account the effect of the source term (ten Thije Boonkkamp and Anthonissen, J Sci Comput 46(1): 47-70, 2011). For a three-dimensional conservation law this results in a 27point coupling for the unknown as well as the source term. Direct solution of the sparse linear systems that arise in 3D ADR problems is not feasible due to fill-in. Iterative solution of such linear systems remains to be the only efficient alternative which requires less memory and shorter time to solution compared to direct solvers. Iterative solvers require a preconditioner to reduce the number of iterations. We present results using several different preconditioning techniques and study their effectiveness.

Subject Keywords

Systems

URI

https://hdl.handle.net/11511/38634

DOI

https://doi.org/10.1007/978-3-319-39929-4_27

Collections

Department of Computer Engineering, Conference / Seminar

Suggestions

OpenMETU
Core

Gauge covariance and spin-current conservation in the gauge-field formulation of systems with spin–orbit coupling Shikakhwa, M S; Turgut, Sadi; Pak, N K (IOP Publishing, 2012-2-23) The question of gauge covariance in the non-Abelian gauge-field formulation of two space-dimensional systems with spin-orbit coupling relevant to spintronics is investigated. Although these are generally gauge-fixed models, it is found that for the class of gauge fields that are spacetime independent and satisfy a U(1) algebra, thus having a vanishing field strength, there is a residual gauge freedom in the Hamiltonian. The gauge transformations assume the form of a space-dependent rotation of the transform...
AN INTEGRABLE FAMILY OF MONGE-AMPERE EQUATIONS AND THEIR MULTI-HAMILTONIAN STRUCTURE NUTKU, Yavuz; Sarıoğlu, Bahtiyar Özgür (1993-01-01) We have identified a completely integrable family of Monge-Ampère equations through an examination of their Hamiltonian structure. Starting with a variational formulation of the Monge-Ampère equations we have constructed the first Hamiltonian operator through an application of Dirac's theory of constraints. The completely integrable class of Monge-Ampère equations are then obtained by solving the Jacobi identities for a sufficiently general form of the second Hamiltonian operator that is compatible with the...
Explaining the relationship between high school students' selected affective characterstics and their physics achievement Doğan Tekiroğlu, Özlem; Eryılmaz, Ali; Department of Secondary Science and Mathematics Education (2005) The purpose of this study is to investigate the relationship between some of selected affective characteristics of high school students related to physics lesson and their physics achievement in electricity concept. These affective characteristics of the students includes their interest in physics, importance of physics, enjoyment of extra-curricular activities related to physics, physics course anxiety, physics test anxiety, achievement motivation in physics, student motivation in physics, self-efficacy in...
NEW APPROACH TO THE PATH-INTEGRAL REPRESENTATION FOR THE DIRAC PARTICLE PROPAGATOR Alıyev, Tahmasıb; PAK, NK (1994-11-15) The path integral representation for the propagator of a spinning particle in an external electromagnetic field is derived using the functional derivative formalism with the help of a Weyl symbol representation. The proposed method essentially simplifies the proof of the path integral representation starting from the equation for the Green function and automatically leads to a precise and unambiguous form of the boundary conditions for the Grassmann variables and puts a strong restriction on the choice of t...
Time-constrained temporal logic control of multi-affine systems Aydın Göl, Ebru (Elsevier BV, 2013-11-01) In this paper, we consider the problem of controlling a dynamical system such that its trajectories satisfy a temporal logic property in a given amount of time. We focus on multi-affine systems and specifications given as syntactically co-safe linear temporal logic formulas over rectangular regions in the state space. The proposed algorithm is based on estimating the time bounds for facet reachability problems and solving a time optimal reachability problem on the product between a weighted transition syste...

Citation Formats

A. A. Sivas, M. Manguoğlu, J. H. M. t. T. Boonkkamp, and M. J. H. Anthonissen, “Discretization and Parallel Iterative Schemes for Advection-Diffusion-Reaction Problems,” 2015, vol. 112, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/38634.