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Utilizing neural networks to supplant chemical kinetics tabulation through mass conservation and weighting of species depletion

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Energy and AI 2024年第2期16卷 101-110页

作者： Franz M.Rohrhofer Stefan Posch Clemens Gößnitzer JoséM.García-Oliver Bernhard C.Geiger Know-Center GmbH Sandgasse 36Graz8010StyriaAustria LEC GmbH Inffeldgasse 19Graz8010StyriaAustria Universitat Politècnica de València Camíde VeraValència46022ValènciaSpain

Artificial Neural Networks(ANNs)have emerged as a powerful tool in combustion simulations to replace memory-intensive tabulation of integrated chemical *** reaction mechanisms,however,present a challenge for standard ANN approaches as modeling multiple species typically suffers from inaccurate predictions on minor *** paper presents a novel ANN approach which can be applied on complex reaction mechanisms in tabular data form,and only involves training a single ANN for a complete reaction *** approach incorporates a network architecture that automatically conserves mass and employs a particular loss weighting based on species *** modifications are used to improve the overall ANN performance and individual prediction accuracies,especially for minor species mass *** validate its effectiveness,the approach is compared to standard ANNs in terms of performance and ANN *** distinct reaction mechanisms(H_(2),C_(7)H_(16),C_(12)H_(26),OME_(34))are used as a test cases,and results demonstrate that considerable improvements can be achieved by applying both modifications.

关键词： Neural network approach Chemical kinetics Flamelet tabulation mass conservation Species loss weighting

Discrete mass conservation and stability analysis of the ocean-atmosphere model with coupling conditions

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Journal of Ocean Engineering and Science 2023年第6期8卷 577-589页

作者： Taj Munir Anwarud Din Saif Ullah M.Y.Malik A.S.Alqahtani Abus Salam School of mathematical sciences GC University68-BLahore 54600Pakistan Department of Mathematics Sun Yat-sen University Guangzhou 510275P.R.China Department of Mathematics Government College UniversityLahore54000Pakistan Department of Mathematics College of SciencesKing Khalid UniversityAbha61413 Kingdom of Sauidi Arabia

In this work we considered bi-domain partial differential equations(PDEs)with two coupling interface *** one domain is corresponding to the ocean and the second is to the *** two coupling conditions are used to linked the interaction between these two *** we know that almost every engineering problem modeled via *** analytical solutions of these kind of problems are not easy,so we use numerical *** this study we discuss the two essential properties,namely mass conservation and stability analysis of two types of coupling interface conditions for the oceanatmosphere *** coupling conditions arise in general circulation models used in climate *** two coupling conditions are the Dirichlet-Neumann and bulk interface *** the stability analysis,we use the Godunov-Ryabenkii theory of normal-mode *** main empha-sis of this work is to study the numerical properties of coupling conditions and an important point is to maintain conservativity of the overall ***,for the numerical approximation we use two methods,an explicit and implicit *** implicit coupling have further two algorithms,monolithic algorithm and partitioned iterative *** partitioned iterative approach is complex as compared to the monolithic *** addition,the comparison of the numerical results are exhibited through graphical illustration and simulation results are drafted in tabular form to validate our theoretical *** novel characteristics of the findings from this paper can be of great importance in science and ocean engineering.

关键词： Stability analysis mass conservation Explicit coupling methods Implicit coupling methods Ocean-atmosphere coupling

Solving coupled nonlinear Schrödinger equations via a direct discontinuous Galerkin method

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Chinese Physics B 2012年第3期21卷 10-14页

作者：张荣培蔚喜军冯涛 School of Sciences Liaoning Shihua University Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics

In this work,we present the direct discontinuous Galerkin(DDG) method for the one-dimensional coupled nonlinear Schrdinger(CNLS) *** prove that the new discontinuous Galerkin method preserves the discrete mass conservations corresponding to the properties of the CNLS *** ordinary differential equations obtained by the DDG space discretization is solved via a third-order stabilized Runge-Kutta *** experiments show that the new DDG scheme gives stable and less diffusive results and has excellent long-time numerical behaviors for the CNLS equations.

关键词： direct discontinuous Galerkin method coupled nonlinear Schrdinger equation mass conservation

Improved conservative level set method for free surface flow simulation

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Journal of Hydrodynamics 2014年第2期26卷 316-325页

作者：赵兰浩毛佳刘晓青 BAI Xin WILLIAMS J. J. R. College of Water Conservancy and Hydropower Engineering Hohai University School of Engineering and Materials Science Queen Mary University of London

By coupling the standard and the conservative level set methods, an improved conservative level set method is proposed to capture the free surface smoothly with excellent mass conservation properties. The improvement lies in the fact that the surface normal is computed from a signed distance function instead of the Heaviside function. Comparing with the conservative level set method, the inevitable numerical discretization errors to point the surface normal in arbitrary directions could be eliminated, and the instability of the numerical solution could be improved efficiently. The advantage is clear in the straightforward combination of the standard level set and the conservative level set and a little effort is taken in coding compared with other coupled methods. The present method is validated with several well-known benchmark problems, including the 2-D Zalesak＇s disk rotating, the 3-D sphere stretching in deformation vortex and the dam break flow simulation. The results are shown to be in good agreement with the published experimental data and numerical results.

关键词： flee surface flow improved conservative level set mass conservation

Third-order unconditional positivity-preserving schemes for reactive flows keeping both mass and mole balance

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Chinese Journal of Aeronautics 2023年第11期36卷 24-41页

作者： Jianhua PAN Luxin Li Zhejiang Provincial Engineering Research Center for the Safety of Pressure Vessel and Pipeline Ningbo UniversityNingbo 315211China Key Laboratory of Impact and Safety Engineering Ministry of EducationNingbo UniversityNingbo 315211China

In this paper,the previously proposed second-order process-based modified Patankar Runge-Kutta schemes are extended to the third order of *** to the process-based implicit handling of reactive source terms,the mass conservation,mole balance and energy conservation are kept simultaneously while the positivity for the density and pressure is preserved unconditionally even with stiff reaction *** is proved that the first-order truncation terms for the Patankar coefficients must be zero to achieve a prior third order of accuracy for most cases.A twostage Patankar procedure for each Runge-Kutta step is designed to eliminate the first-order truncation terms,accomplish the prior third order of accuracy and maximize the Courant number which the total variational diminishing property *** the same approach as the second-order schemes,the third-order ones are applied to Euler equations with chemical reactive source *** studies including both 1D and 2D ordinary and partial differential equations are conducted to affirm both the prior order of accuracy and the positivity-preserving property for the density and pressure.

关键词： Chemical reactions Positivity-preserving Patankar schemes mass conservation Mole balance Third-order schemes

An Adaptive Time-Stepping Strategy for the Cahn-Hilliard Equation

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Communications in Computational Physics 2012年第4期11卷 1261-1278页

作者： Zhengru Zhang Zhonghua Qiao Laboratory of Mathematics and Complex Systems Ministry of EducationSchool of Mathematical SciencesBeijing Normal UniversityBeijing 100875China Institute for Computational Mathematics&Department of Mathematics Hong Kong Baptist UniversityKowloon TongHong Kong

This paper studies the numerical simulations for the Cahn-Hilliard equation which describes a phase separation *** numerical simulation of the Cahn-Hilliardmodel needs very long time to reach the steady state,and therefore large time-stepping methods become *** main objective of this work is to construct the unconditionally energy stable finite difference scheme so that the large time steps can be used in the numerical *** equation is discretized by the central difference scheme in space and fully implicit second-order scheme in *** proposed scheme is proved to be unconditionally energy stable and *** error estimate for the numerical solution is also obtained with second order in both space and *** using this energy stable scheme,an adaptive time-stepping strategy is proposed,which selects time steps adaptively based on the variation of the free energy against *** numerical experiments are presented to demonstrate the effectiveness of the adaptive time-stepping approach.

关键词： Adaptive time-stepping unconditionally energy stable Cahn-Hilliard equation mass conservation

Stabilized Crouzeix-Raviart element for the coupled Stokes and Darcy problem

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Applied Mathematics and Mechanics(English Edition) 2010年第3期31卷 393-404页

作者：冯民富祁瑞生朱瑞鞠炳焘 Department of Mathematics Sichuan University Department of Information Technology CNOOC Energy Technology and Services Limited Beijing Branch Company

This paper introduces a new stabilized finite element method for the coupled Stokes and Darcy problem based on the nonconforming Crouzeix-Raviart element. Optimal error estimates for the fluid velocity and pressure ar... 详细信息

关键词： Beavers-Joseph-Saffman condition mass conservation balance of force,coupled Stokes and Darcy problem

A Conservative Modification to the Ghost Fluid Method for Compressible Multiphase Flows

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Communications in Computational Physics 2011年第9期10卷 785-806页

作者： Wei Liu Li Yuan Chi-Wang Shu Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China Division of Applied Mathematics Brown UniversityProvidence RI 02912USA.

A conservative modification to the ghost fluid method(GFM)is developed for compressible multiphase *** motivation is to eliminate or reduce the conservation error of the GFM without affecting its *** track the conservative variables near the material interface and use this information to modify the numerical solution for an interfacing cell when the interface has passed the *** modification procedure can be used on the GFM with any base *** this paper we use the fifth order finite difference WENO scheme for the spatial discretization and the third order TVD Runge-Kutta method for the time *** level set method is used to capture the *** experiments show that the method is at least mass and momentum conservative and is in general comparable in numerical resolution with the original GFM.

关键词： WENO scheme ghost fluid method(GFM) mass conservation multiphase flow

A Conservative SAV-RRK Finite Element Method for the Nonlinear Schrodinger Equation

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Advances in Applied Mathematics and Mechanics 2023年第3期15卷 583-601页

作者： Jun Yang Nianyu Yi School of Mathematics and Computational Science Xiangtan UniversityXiangtanHunan 411105China Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan UniversityXiangtanHunan 411105China

*** this paper,we propose,analyze and numerically validate a conservative finite element method for the nonlinear Schrodinger equation.A scalar auxiliary variable(SAV)is introduced to reformulate the nonlinear Schrodinger equation into an equivalent system and to transform the energy into a quadratic *** use the standard continuous finite element method for the spatial discretization,and the relaxation Runge-Kutta method for the time *** mass and energy conservation laws are shown for the semi-discrete finite element scheme,and also preserved for the full-discrete scheme with suitable relaxation coefficient in the relaxation Runge-Kutta *** examples are presented to demonstrate the accuracy of the proposed method,and the conservation of mass and energy in long time simulations.

关键词： Schrodinger equation mass conservation energy conservation finite element method relaxation Runge-Kutta scalar auxiliary variable