A Hybrid Finite Volume/PDF Monte Carlo Method to Capture Sharp Gradients in Unstructured Grids

2000 ◽  
Author(s):  
Genong Li ◽  
Michael F. Modest
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Finite Volume ◽  
Solution Procedure ◽  
Reactive Flow ◽  
Diffusion Combustion ◽  
Monte Carlo Code ◽  
Adaptive Grids ◽  
Time Step ◽  
Particle Tracing

Abstract The hybrid finite volume/PDF Monte Carlo method has both the advantages of the finite volume method’s efficiency in solving flow fields and the PDF method’s exactness in dealing with chemical reactions. It is, therefore, increasingly used in turbulent reactive flow calculations. In order to resolve the sharp gradients of flow velocities and/or scalars, fine grids or unstructured solution -adaptive grids have to be used in the finite volume code. As a result, the calculation domain is covered by a grid system with very large variations in cell size. Such grids present a challenge for a combined PDF/Monte Carlo code. To date, PDF calculations have generally been carried out with large cells, which assure that each cell has a statistically meaningful number of particles. Smaller cells would lead to smaller numbers of particles and correspondingly larger statistical errors. In this paper, a particle tracing scheme with adaptive time step and particle splitting and combination is developed, which allows the PDF/Monte Carlo code to use any grid that is constructed in the finite volume code. This relaxation of restrictions on the grid makes it possible to couple PDF/Monte Carlo methods to all popular commercial CFD codes and, consequently, extend existing CFD codes’ capability to simulate turbulent reactive flow in a more accurate way. To illustrate the solution procedure, a PDF/ Monte Carlo code is combined with FLUENT to solve a turbulent diffusion combustion problem in an axisymmetric channel.

AN EFFICIENT METHOD TO CALCULATE FIELD THEORIES WITH DYNAMICAL FERMIONS

1991 ◽  
Vol 02 (02) ◽  
pp. 561-600 ◽  
Author(s):  
MARCIA G. DO AMARAL ◽  
M. KISCHINHEVSKY ◽  
C. ARAGÃO DE CARVALHO ◽  
F.L. TEIXEIRA
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Fourth Order ◽  
Efficient Method ◽  
Field Theories ◽  
Step Size ◽  
Time Step ◽  
Acceptance Probability ◽  
Hybrid Monte Carlo ◽  
Time Step Size

We discuss the application of the Hybrid Monte Carlo method for models that describe conducting polymers, namely the Su-Schrieffer-Heeger and the Krive-Rozhavskii models. We use a fourth order Leap Frog algorithm, in order to decrease the number of Monte Carlo rejections. We also make a detailed study of which solver has the best performance in each phase of the theory as well as the dependence of the acceptance probability as a function of the time step size and other parameters.

Using the Few-Group Approximation for Calculating Some Neutron-Physical Characteristics of VVER-1000 Core by Means of the MCU Monte-Carlo Code

2021 ◽  
Author(s):  
Artem S. Bikeev ◽  
Yulia S. Daichenkova ◽  
Mikhail A. Kalugin ◽  
Denis Shkarovsky ◽  
Vladislav V. Shkityr
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Cross Sections ◽  
Optimal Number ◽  
Physical Characteristics ◽  
Monte Carlo Code ◽  
Special Version ◽  
The Monte Carlo Method ◽  
Scattering Anisotropy ◽  
Neutron Cross Sections

Abstract The main purpose of this work is to study the possibility of using the few-group approximation for calculation of some neutron-physical characteristics of VVER-1000 core by means of special version of MCU code. The Monte-Carlo method for VVER-1000 core neutron-physical characteristics calculation using the few-group approximation with an estimate of neutron cross sections “by location“ was provided and tested in this research. The reduction of calculation time due to the transition from a pointwise model of representation of cross sections to the few-group approximation and methodical error of this approach were evaluated. Optimal number of energy groups was determined. It was found that consideration of the scattering anisotropy leads to a significant decrease in methodical error. Ways of further reduction of methodical error were worked out.

DEVELOPMENT OF A HIGHER-ORDER ACCURATE RECONSTRUCTION SCHEME WITH REDUCED LEAST SQUARE MATRIX FOR CONVECTIVE AND DIFFUSIVE FLUX EVALUATION

2009 ◽  
Vol 06 (03) ◽  
pp. 425-446 ◽  
Author(s):  
PRAVEEN NAIR ◽  
T. JAYACHANDRAN ◽  
BHAL CHANDRA PURANIK ◽  
V. UPENDRA BHANDARKAR
Keyword(s):  
Finite Volume ◽  
Higher Order ◽  
Least Square ◽  
Test Facility ◽  
Adaptive Grids ◽  
Computationally Efficient ◽  
Time Step ◽  
Reconstruction Scheme ◽  
The Matrix ◽  
Square Matrix

The development of a higher-order reconstruction scheme with reduced least square matrix is presented. The matrix used in conventional least square based reconstruction schemes for finite volume solvers contains bigger terms. For solution dependent schemes, this matrix has to be inverted for each time step, which is computationally costlier. To overcome this, certain mathematical principles applicable to finite volume formulation, have been used to eliminate a good number of terms appearing in the matrix. In addition, accurate and computationally efficient derivative plug-ins are incorporated to make the formulation generalized so that one can extend it to any order of accuracy. The presence of higher derivative terms in this scheme ensures uniformly higher-order accuracy throughout the flow domain. The reduced matrix can be used for data independent as well as solution dependent reconstruction schemes. Computationally efficient stencil searching algorithm, satisfying physical and topological requirements and capable of handling structured, unstructured, and adaptive grids has been coupled with the scheme. The scheme has been successfully used to simulate flow over blunt cone-flare, NASA B2 nozzle, and high altitude test facility. The solver has shown around 30% saving in least square matrix evaluation time.

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