Page 39 - Krész, Miklós, and Andrej Brodnik (eds.). MATCOS-13. Proceedings of the 2013 Mini-Conference on Applied Theoretical Computer Science. Koper: University of Primorska Press, 2016.
P. 39
numerical simulation of filtration gas combustion
processes on the shared memory machines.
Tatyana Kandryukova
Institute of Computational Mathematics and Mathematical Geophysics SB RAS
630090, prospect Akademika Lavrentjeva, 6
Novosibirsk, Russia
kandryukova@labchem.sscc.ru
ABSTRACT In particular low-speed mode of filtration gas combustion
This work is devoted to the searh of the efficient algorithms process, which is under consideration, is the physical basis
for the simulation of filtration gas combustion processes. In for construction modern industrial flame arrester, environ-
particular, a two-level parallel algorithm based on the ex- mentally friendly burners and other. Therefore numerical
plicit finite difference scheme using an adaptive mesh is con- simulation of FGC is the problem of current interest that
structed. Two ways of parallelization, namely, the direct has important practical application.
usage of OpenMP directives and special distribution of data From the physical point of view the process presents the
across threads are carried out. It is numerically shown, that propagation of the region of gaseous exothermic reaction in
the last one provides significant performance advantage. chemically inert porous medium, as gaseous reactants are
being supplied into the region of chemical transformation
Categories and Subject Descriptors [2]. It is implemented as follows. Let there be a tube filled
with a porous material, measuring about 10 cm. From one
D.1.3 [Programming Techniques]: Concurrent Program- edge of it a combustible gas mixture is supplied at a rate of
ming; G.1 [Numerical Analysis]: Miscellaneous; J.2 [Physical v. Then the mixture is ignited, resulting in a flat combustion
Sciences And Engineering]: Mathematics and statistics, front, which can either be stationary or move in any direc-
Physics, Chemistry tion (at a rate of u), depending on the model parameters
General Terms (see Figure 1). It occurs due to the heat recuperation. In
the heating zone fresh gas mixture gets hot and the chemical
Algorithms, Performance process occurs in the reaction zone that causes heat release.
In the relaxation zone high-temperature products of com-
Keywords bustion exchange heat with the porous solid and then heat
transfers through it back to the heating zone by means of
Combustion wave, explicit difference schemes, adaptive grids, thermal conduction.
parallelization on shared memory, OpenMP-threads
Supervisor Figure 1: The scheme of the physical model of FGC
Yuri Laevsky The main difficulty in the simulation of this process is its
Institute of Computational Mathematics and Mathematical very different scales; it is especially hard to deal with the
Geophysics SB RAS kinetic-diffusion distinction.
630090, prospect Akademika Lavrentjeva, 6 In this study the simplest case is considered, when the model
Novosibirsk, Russia is one-dimensional, and still it takes hours to simulate the
process that lasts less than a half of a minute. It doesn’t
1. INTRODUCTION seem possible to proceed to multidimensional case under
such conditions. At the present time great expectations for
The phenomena of filtration gas combustion (FGC) had having the opportunity to deal with such tasks are related
been discovered in the 70s of the previous century and it to the appearance of multi-processor machines and the de-
has still not been studied fully. Meanwhile the knowledge of velopment of parallel methods.
the properties of FGC processes is essential in solving many This work is an expansion of [3] and devoted to the analysis
problems of chemical technology, ecology, fire safety, etc. of the possibilities to improve the performance of some com-
putational models of FGC in low-speed mode. In particular
the introduction of adaptive nested grid [5] and paralleliza-
m a t c o s -1 3 Proceedings of the 2013 Mini-Conference on Applied Theoretical Computer Science 39
Koper, Slovenia, 10-11 October
processes on the shared memory machines.
Tatyana Kandryukova
Institute of Computational Mathematics and Mathematical Geophysics SB RAS
630090, prospect Akademika Lavrentjeva, 6
Novosibirsk, Russia
kandryukova@labchem.sscc.ru
ABSTRACT In particular low-speed mode of filtration gas combustion
This work is devoted to the searh of the efficient algorithms process, which is under consideration, is the physical basis
for the simulation of filtration gas combustion processes. In for construction modern industrial flame arrester, environ-
particular, a two-level parallel algorithm based on the ex- mentally friendly burners and other. Therefore numerical
plicit finite difference scheme using an adaptive mesh is con- simulation of FGC is the problem of current interest that
structed. Two ways of parallelization, namely, the direct has important practical application.
usage of OpenMP directives and special distribution of data From the physical point of view the process presents the
across threads are carried out. It is numerically shown, that propagation of the region of gaseous exothermic reaction in
the last one provides significant performance advantage. chemically inert porous medium, as gaseous reactants are
being supplied into the region of chemical transformation
Categories and Subject Descriptors [2]. It is implemented as follows. Let there be a tube filled
with a porous material, measuring about 10 cm. From one
D.1.3 [Programming Techniques]: Concurrent Program- edge of it a combustible gas mixture is supplied at a rate of
ming; G.1 [Numerical Analysis]: Miscellaneous; J.2 [Physical v. Then the mixture is ignited, resulting in a flat combustion
Sciences And Engineering]: Mathematics and statistics, front, which can either be stationary or move in any direc-
Physics, Chemistry tion (at a rate of u), depending on the model parameters
General Terms (see Figure 1). It occurs due to the heat recuperation. In
the heating zone fresh gas mixture gets hot and the chemical
Algorithms, Performance process occurs in the reaction zone that causes heat release.
In the relaxation zone high-temperature products of com-
Keywords bustion exchange heat with the porous solid and then heat
transfers through it back to the heating zone by means of
Combustion wave, explicit difference schemes, adaptive grids, thermal conduction.
parallelization on shared memory, OpenMP-threads
Supervisor Figure 1: The scheme of the physical model of FGC
Yuri Laevsky The main difficulty in the simulation of this process is its
Institute of Computational Mathematics and Mathematical very different scales; it is especially hard to deal with the
Geophysics SB RAS kinetic-diffusion distinction.
630090, prospect Akademika Lavrentjeva, 6 In this study the simplest case is considered, when the model
Novosibirsk, Russia is one-dimensional, and still it takes hours to simulate the
process that lasts less than a half of a minute. It doesn’t
1. INTRODUCTION seem possible to proceed to multidimensional case under
such conditions. At the present time great expectations for
The phenomena of filtration gas combustion (FGC) had having the opportunity to deal with such tasks are related
been discovered in the 70s of the previous century and it to the appearance of multi-processor machines and the de-
has still not been studied fully. Meanwhile the knowledge of velopment of parallel methods.
the properties of FGC processes is essential in solving many This work is an expansion of [3] and devoted to the analysis
problems of chemical technology, ecology, fire safety, etc. of the possibilities to improve the performance of some com-
putational models of FGC in low-speed mode. In particular
the introduction of adaptive nested grid [5] and paralleliza-
m a t c o s -1 3 Proceedings of the 2013 Mini-Conference on Applied Theoretical Computer Science 39
Koper, Slovenia, 10-11 October
