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A Finite Volume Method with unstructured triangular grids for Numerical Modeling of Tidal Current

China Ocean Engineering 2005年第4期19卷 693-700页

作者：史宏达刘臻 Engineering College Ocean University of China Qingdao 266071China

The finite volume method （FVM） has many advantages in 2-D shallow water numerical simulation. In this study, the finite volume method is used with unstructured triangular grids to simulate the tidal currents. The Roe scheme is applied in the calculation of the intercell numerical flux, and the MUSCL method is introduced to improve its accuracy. The time integral is a two-step scheme of forecast and revision. For the verification of the present method, the Stoker＇s problem is calculated and the result is compared with the mathematically analytic solutions. The comparison indicates that the method is feasible. A sea area of a port is used as an example to test the method established here. The result shows that the present computational method is satisfactory, and it could be applied to the engineering fields.

关键词： finite volume method numerical modeling unstructured triangular grids tidal currents

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Finite volume method with unstructured triangular grids for numerical modeling of tidal current

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China Ocean Engineering 2005年第4期19卷 693-700页

作者： Shi, Hong-Da Liu, Zhen Engineering College Ocean University of China Qingdao 266071 China

The finite volume method (FVM) has many advantages in 2-D shallow water numerical simulation. In this study, the finite volume method is used with unstructured triangular grids to simulate the tidal currents. The Roe scheme is applied in the calculation of the intercell numerical flux, and the MUSCL method is introduced to improve its accuracy. The time integral is a two-step scheme of forecast and revision. For the verification of the present method, the Stoker's problem is calculated and the result is compared with the mathematically analytic solutions. The comparison indicates that the method is feasible. A sea area of a port is used as an example to test the method established here. The result shows that the present computational method is satisfactory, and it could be applied to the engineering fields.

关键词： Finite volume method Numerical modeling Tided currents unstructured triangular grids

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A fourth-order compact finite volume method on unstructured grids for simulation of two-dimensional incompressible flow

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JOURNAL OF COMPUTATIONAL PHYSICS 2025年 520卷

作者： Wen, Ling Yang, Yan-Tao Cai, Qing-Dong Peking Univ Coll Engn Dept Mech & Engn Sci State Key Lab Turbulence & Complex Syst Beijing 100871 Peoples R China

This paper introduces a novel and efficient compact reconstruction procedure for high-order finite volume methods applied to unstructured grids. In this procedure, we establish a set of constitutive relations that ensure the continuity of the reconstruction polynomial and its normal derivatives between adjacent elements at control points. The paper delves into the details of the fourth-order compact reconstruction method specifically designed for two-dimensional triangular grids. This method can be considered an extension of the one-dimensional compact scheme and cubic spline interpolation methods to two-dimensional triangular unstructured grids. In the cubic polynomial reconstruction, a two-dimensional cubic polynomial is reconstructed using the cell averages of elements in the standard stencil and the function values at control points. The determination of function values at control points is achieved by adhering to the constraint of normal derivative continuity. This reconstruction is solved using a relaxation iteration method and has been verified to be solvable for triangular grids. Compared to other fourth-order implicit compact polynomial reconstructions, our method requires solving a smaller number of unknowns, which means less computational cost in reconstruction. By applying this method to solve the Poisson equation, the linear convection equation, and incompressible flow benchmarks, it demonstrates that the proposed method exhibits the expected high-order accuracy and performs well in incompressible flow problems.

关键词： unstructured triangular grids Finite volume method High order Compact reconstruction Incompressible flow

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unstructured triangular cellular automata for modeling geographic spread

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APPLIED MATHEMATICS AND COMPUTATION 2015年 258卷 520-536页

作者： Ortigoza, Gerardo M. Univ Veracruzana Fac Ingn Boca Del Rio Ver Mexico

In this work we propose the use of a cellular automata defined on unstructured triangular grids to simulate geographic spread. A grid structure of a finite element implementation is adopted to cellular automata computations. This approach allow us to model and simulate with cellular automata on computational domains with complex geometries (polygonal boundaries), it still retains the easy implementation of cellular automata and does not present the anisotropy induced by regular grids. We show a comparison (storage and number of evaluations required) of our approach with the classical cellular automata implementations on regular grids: rectangular, equilateral triangulation and hexagonal. The geographical spread on unstructured triangular grids is presented by defining two simple cellular automata models a binary spread (two states) and a deforestation spread (three states). Using unstructured triangular grids no anisotropy effects induced by grid and neighborhood are presented;circular fronts spread as circular fronts. Moreover, the use of unstructured triangular grids for cellular automata can simplifies the coupling of cellular automata with other numerical techniques such as finite element or finite volume. (C) 2015 Elsevier Inc. All rights reserved.

关键词： Cellular automata unstructured triangular grids Anisotropy

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Numerical Modeling of Plasma Devices by the Particle-In-Cell Method on unstructured grids

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Mathematical Models and Computer Simulations 2018年第2期10卷 198-208页

作者： Dikalyuk, A.S. Kuratov, S.E. All-Russia Research Institute of Automatics (VNIIA) Moscow Russian Federation Institute for Problems of Mechanics (IPMech) Russian Academy of Sciences (RAS) Moscow Russian Federation Moscow Institute of Physics and Technology (MIPT) Moscow Russian Federation

The paper considers methods and algorithms providing the basis for a computer program implementing an axial-symmetric electrostatic version of the particle-in-cell method on unstructured triangular grids. In the presented implementation, the Poisson equation is approximated using the finite volume method. A discrete analog of the Poisson equation is solved by the multigrid method. Charged particle trajectories are calculated using the Boris method. Methods for interpolating electrostatic fields on unstructured grids and obtaining the charge density in the computational domain are considered. Special attention is paid to the specifics of implementing these methods in axisymmetric geometry. The developed computer code is tested on the problem of a flat diode operating in the space charge mode. © 2018, Pleiades Publishing, Ltd.

关键词： particle-in-cell method two-dimensional Child–Langmuir problem unstructured triangular grids

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Modelling and simulating Chikungunya spread with an unstructured triangular cellular automata

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Infectious Disease Modelling 2020年第1期5卷 197-220页

作者： Gerardo Ortigoza Fred Brauer Iris Neri Facultad de Ingeniería Universidad VeracruzanaBoca Del RíoVerMexico Mathematics Department University of British ColumbiaVancouverB.CCanada Maestría en Gestion Integrada de Cuencas Universidad Autonoma de QueretaroMexico

In this work we propose a mathematical model to simulate Chikungunya spread;the spread model is implemented in a C++ cellular automata code defined on unstructured triangular grids and space visualizations are performed with *** order to simulate the time space spread of the Chikungunya diseases we include assumptions such as:heterogeneous human and vector densities,population mobility,geographically localized points of infection using geographical information systems,changes in the probabilities of infection,extrinsic incubation and mosquito death rate due to environmental *** experiments reproduce the qualitative behavior of diseases spread and provide an insight to develop strategies to prevent the diseases spread.

关键词： Cellular automata unstructured triangular grids Chikungunya spread

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Estimation of wave responses from subvertical macrofracture systems using a grid characteristic method

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Mathematical Models and Computer Simulations 2013年第5期5卷 479-491页

作者： Muratov, M.V. Petrov, I.B. Moscow Physical-Technical Institute (State University) Moscow Russian Federation

This work investigates the formation and propagation of scattered waves forming a response of crack structures on the seismologic record. The initial impulse is a flat wave front propagating into the depth of the medium. The paper considers the periodic structure of the scattered wave response from a system (cluster) of subvertical cracks. The procedures of estimation of geometrical parameters of such crack structures are based on numerical experiments. We use a grid-characteristic method to calculate the triangular grids with the formulation of boundary conditions at the interface of the medium and the cracks, as well as on the borders of the region of integration with the characteristic properties of the governing equations of the hyperbolic type. This numerical method makes it possible to build the most correct numerical algorithms on the boundaries of the integration domain and on the surfaces of the media division (interfaces) and to take into account the domain of the solution’s dependence and the physics of the problem (propagation of disturbances on the characteristic directions). This is why this method is perhaps the most suitable one for the numerical solution of dynamic problems with a distinct wave character in geologically substantially inhomogeneous media, in particular, for the considered problem of seismic waves interaction with fissured structures. © 2013, Pleiades Publishing, Ltd.

关键词： fissured structures grid-characteristic method hyperbolic systems of equations numerical simulation prospecting seismology unstructured triangular grids

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ACFUEGOS: An unstructured triangular Cellular Automata for Modelling Forest Fire Propagation 6th

ACFUEGOS: An Unstructured Triangular Cellular Automata for M...

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6th International Conference on Supercomputing in Mexico (ISUM)

作者： Ortigoza, Gerardo M. Lorandi, Alberto Neri, Iris Univ Veracruzana Fac Ingn Boca Del Rio Veracruz Mexico Univ Veracruzana Inst Ingn Boca Del Rio Veracruz Mexico

ISBN: (纸本)9783319322438;9783319322421

In this work we propose the use of a cellular automata defined on unstructured triangular grids to simulate forest fire propagation. This approach allow us to model computational domains with complex geometries (polygonal boundaries). It still retains the easy implementation of cellular automata and it does not present the anisotropy induced by regular grids. The forest fire spread is modeled by using ignition and stop burning probabilities. The computational domain is discretized by an unstructured triangular grid;each cell (triangle) assumes four states: non flamable, unburned fuel, burning and burned. Ignition probabilities for grass, shrubs and timber are estimated assuming Anderson's 13 fuel models and a maximum rate of spread. These probabilities are modified by the effects of different variables such as: slope, wind (direction/intensity), relative humidity and ambient temperature. The cellular automata code was implemented in C++, the serial runnigs of the code were performed in an Intel Core CPU 2.90 GHz 8 processors workstation. The numerical simulations reproduce the qualitative behavior of forest fires under the effect of type of fuel, slope and wind (direction/intensity).

关键词： Cellular automata unstructured triangular grids Forest fire Spotting

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