Pub Date : 2020-06-06DOI: 10.1080/23324309.2020.1785893
Gaël Poëtte, Xavier Valentin, Adrien Bernede
Abstract Monte Carlo (MC) schemes for photonics have been intensively studied throughout the past decades. The recent ISMC scheme presents many advantages (no teleportation error, converging behavior with respect to the spatial and time discretisations). But it is rather different from the IMC one (it is based on a different linearization and needs a slightly different code architecture). On another hand, legacy codes are often based on IMC implementations. For this reason, it remains important to be able to cancel the teleportation error within IMC codes. Canceling the teleportation error within the IMC framework is also important for fair comparisons between both the IMC and the ISMC linearisations. This paper aims at suggesting some simple corrections to apply to an IMC implementation to completely cancel the teleportation error.
{"title":"Canceling Teleportation Error in Legacy IMC Code for Photonics (Without Tilts, With Simple Minimal Modifications)","authors":"Gaël Poëtte, Xavier Valentin, Adrien Bernede","doi":"10.1080/23324309.2020.1785893","DOIUrl":"https://doi.org/10.1080/23324309.2020.1785893","url":null,"abstract":"Abstract Monte Carlo (MC) schemes for photonics have been intensively studied throughout the past decades. The recent ISMC scheme presents many advantages (no teleportation error, converging behavior with respect to the spatial and time discretisations). But it is rather different from the IMC one (it is based on a different linearization and needs a slightly different code architecture). On another hand, legacy codes are often based on IMC implementations. For this reason, it remains important to be able to cancel the teleportation error within IMC codes. Canceling the teleportation error within the IMC framework is also important for fair comparisons between both the IMC and the ISMC linearisations. This paper aims at suggesting some simple corrections to apply to an IMC implementation to completely cancel the teleportation error.","PeriodicalId":54305,"journal":{"name":"Journal of Computational and Theoretical Transport","volume":"49 1","pages":"162 - 194"},"PeriodicalIF":0.7,"publicationDate":"2020-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/23324309.2020.1785893","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43718821","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-06-06DOI: 10.1080/23324309.2020.1785892
M. El-Hadidy
Abstract This paper presents an expansion of the Probability Density Function (PDF) at any time t for the distribution of the microorganism cells movement on the planar surface. A 2-dimensional random walk process accurately models this movement. These cells move linearly on the surface with constant speed and change their direction after exponentially distributed time intervals. In addition, the path length and the uniformly distributed turn angles are independent. Some statistical properties of the original and bounded known version of this distribution have been provided. The estimated length parameter of the cell size is investigated with a simulation study by using a real data set.
{"title":"On the Random Walk Microorganisms Cells Distribution on a Planar Surface and Its Properties","authors":"M. El-Hadidy","doi":"10.1080/23324309.2020.1785892","DOIUrl":"https://doi.org/10.1080/23324309.2020.1785892","url":null,"abstract":"Abstract This paper presents an expansion of the Probability Density Function (PDF) at any time t for the distribution of the microorganism cells movement on the planar surface. A 2-dimensional random walk process accurately models this movement. These cells move linearly on the surface with constant speed and change their direction after exponentially distributed time intervals. In addition, the path length and the uniformly distributed turn angles are independent. Some statistical properties of the original and bounded known version of this distribution have been provided. The estimated length parameter of the cell size is investigated with a simulation study by using a real data set.","PeriodicalId":54305,"journal":{"name":"Journal of Computational and Theoretical Transport","volume":"49 1","pages":"145 - 161"},"PeriodicalIF":0.7,"publicationDate":"2020-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/23324309.2020.1785892","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42844250","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-05-25DOI: 10.1080/23324309.2020.1842453
K. Amagai, Yuko Hatano, M. Machida
Abstract The linear transport theory is developed to describe the time dependence of the number density of tracer particles in porous media. The advection is taken into account. The transport equation is numerically solved by the analytical discrete ordinates method. For the inverse Laplace transform, the double-exponential formula is employed. In this paper, we consider the travel distance of tracer particles whereas the half-space geometry was assumed in our previous paper [Amagai et al. (2020). Trans. Porous Media 132:311–331].
摘要建立了线性输运理论来描述多孔介质中示踪粒子数密度随时间的变化规律。平流被考虑在内。用解析离散坐标法对输运方程进行了数值求解。对于拉普拉斯逆变换，采用双指数公式。在本文中，我们考虑了示踪粒子的行进距离，而在我们之前的论文[Amagai et al.(2020)]中假设了半空间几何。反式。多孔介质[j]。
{"title":"Linear Transport in Porous Media","authors":"K. Amagai, Yuko Hatano, M. Machida","doi":"10.1080/23324309.2020.1842453","DOIUrl":"https://doi.org/10.1080/23324309.2020.1842453","url":null,"abstract":"Abstract The linear transport theory is developed to describe the time dependence of the number density of tracer particles in porous media. The advection is taken into account. The transport equation is numerically solved by the analytical discrete ordinates method. For the inverse Laplace transform, the double-exponential formula is employed. In this paper, we consider the travel distance of tracer particles whereas the half-space geometry was assumed in our previous paper [Amagai et al. (2020). Trans. Porous Media 132:311–331].","PeriodicalId":54305,"journal":{"name":"Journal of Computational and Theoretical Transport","volume":"50 1","pages":"377 - 389"},"PeriodicalIF":0.7,"publicationDate":"2020-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/23324309.2020.1842453","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42658505","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-05-13DOI: 10.1080/23324309.2021.1894174
J. Kuczek, J. Patel, R. Vasques
Abstract This paper introduces a new acceleration technique for the convergence of the solution of transport problems with highly forward-peaked scattering. The technique is similar to a conventional high-order/low-order (HOLO) acceleration scheme. The Fokker-Planck equation, which is an asymptotic limit of the transport equation in highly forward-peaked settings, is modified and used for acceleration; this modified equation preserves the angular flux and moments of the (high-order) transport equation. We present numerical results using the Screened Rutherford, Exponential, and Henyey–Greenstein scattering kernels and compare them to established acceleration methods such as diffusion synthetic acceleration (DSA). We observe three to four orders of magnitude speed-up in wall-clock time compared to DSA.
{"title":"Modified Fokker-Planck Acceleration for Forward-Peaked Transport Problems in Slab Geometry","authors":"J. Kuczek, J. Patel, R. Vasques","doi":"10.1080/23324309.2021.1894174","DOIUrl":"https://doi.org/10.1080/23324309.2021.1894174","url":null,"abstract":"Abstract This paper introduces a new acceleration technique for the convergence of the solution of transport problems with highly forward-peaked scattering. The technique is similar to a conventional high-order/low-order (HOLO) acceleration scheme. The Fokker-Planck equation, which is an asymptotic limit of the transport equation in highly forward-peaked settings, is modified and used for acceleration; this modified equation preserves the angular flux and moments of the (high-order) transport equation. We present numerical results using the Screened Rutherford, Exponential, and Henyey–Greenstein scattering kernels and compare them to established acceleration methods such as diffusion synthetic acceleration (DSA). We observe three to four orders of magnitude speed-up in wall-clock time compared to DSA.","PeriodicalId":54305,"journal":{"name":"Journal of Computational and Theoretical Transport","volume":"50 1","pages":"430 - 453"},"PeriodicalIF":0.7,"publicationDate":"2020-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/23324309.2021.1894174","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48559778","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-04-15DOI: 10.1080/23324309.2020.1775096
Tom Deakin, Simon McIntosh-Smith, J. Lovegrove, R. Smedley-Stevenson, A. Hagues
Abstract In recent years the computer processors underpinning the large, distributed, workhorse computers used to solve the Boltzmann transport equation have become ever more parallel and diverse. Traditional CPU architectures have increased in core count, reduced in clock speed and gained a deep memory hierarchy. Multiple processor vendors offer a collectively diverse range of both CPUs and GPUs, with the architectures used in the fastest machines in the world ever growing in diversity of many-core architectures. Going forward, the landscape of processor technologies will require our codes to function well across multiple architectures. This ever increasing range of architectures represents a unique challenge for solving the Boltzmann equation using deterministic methods in particular, and so it is important to characterize the performance of those key algorithms across the processor spectrum. The solution of the transport equation is computationally expensive, and so we require well optimized and highly parallel solver implementations in order to solve interesting problems quickly. In this work we explore the performance profiles of deterministic SN transport sweeps for both 3D structured (Cartesian) and unstructured (hexahedral) meshes. The study focuses on the characteristics of computational performance which are responsible for the actual performance of a transport solver.
{"title":"Reviewing the Computational Performance of Structured and Unstructured Grid Deterministic SN Transport Sweeps on Many-Core Architectures","authors":"Tom Deakin, Simon McIntosh-Smith, J. Lovegrove, R. Smedley-Stevenson, A. Hagues","doi":"10.1080/23324309.2020.1775096","DOIUrl":"https://doi.org/10.1080/23324309.2020.1775096","url":null,"abstract":"Abstract In recent years the computer processors underpinning the large, distributed, workhorse computers used to solve the Boltzmann transport equation have become ever more parallel and diverse. Traditional CPU architectures have increased in core count, reduced in clock speed and gained a deep memory hierarchy. Multiple processor vendors offer a collectively diverse range of both CPUs and GPUs, with the architectures used in the fastest machines in the world ever growing in diversity of many-core architectures. Going forward, the landscape of processor technologies will require our codes to function well across multiple architectures. This ever increasing range of architectures represents a unique challenge for solving the Boltzmann equation using deterministic methods in particular, and so it is important to characterize the performance of those key algorithms across the processor spectrum. The solution of the transport equation is computationally expensive, and so we require well optimized and highly parallel solver implementations in order to solve interesting problems quickly. In this work we explore the performance profiles of deterministic SN transport sweeps for both 3D structured (Cartesian) and unstructured (hexahedral) meshes. The study focuses on the characteristics of computational performance which are responsible for the actual performance of a transport solver.","PeriodicalId":54305,"journal":{"name":"Journal of Computational and Theoretical Transport","volume":"49 1","pages":"121 - 143"},"PeriodicalIF":0.7,"publicationDate":"2020-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/23324309.2020.1775096","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43955600","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-04-15DOI: 10.1080/23324309.2020.1770796
Siavash Maniee, Seyed Salman Noorazar
Abstract This article reports a comparative study of the convergence rate of an axially symmetric binary gas flow inside a rotating cylinder using an improved direct simulation Monte Carlo algorithm for rarefied gases (v-DSMC) and the conventional DSMC. Subsequently, a comparison between the convergence behavior of the v-DSMC and analytical data is carried out to scrutinize the validity of the v-DSMC algorithm. This method makes use of a modified collision model of variable hard sphere (VHS) termed Maxwell-VHS, which considers an equal contingency of collision but an arbitrary viscosity variation with temperature, for all adjacent gas particles. The results of the numerical simulation declare the convergence rate of the v-DSMC is noticeably faster than those performed by the conventional DSMC; however, a slight computational error occurs at the same simulation time due to higher accuracy of collision sampling in the conventional DSMC. Moreover, the results show a good agreement between the convergence behaviors of the v-DSMC in comparison with the analytical data.
{"title":"Investigating the Simulation Rate of an Axially Symmetric Rarefied Gas Flow Using v-DSMC","authors":"Siavash Maniee, Seyed Salman Noorazar","doi":"10.1080/23324309.2020.1770796","DOIUrl":"https://doi.org/10.1080/23324309.2020.1770796","url":null,"abstract":"Abstract This article reports a comparative study of the convergence rate of an axially symmetric binary gas flow inside a rotating cylinder using an improved direct simulation Monte Carlo algorithm for rarefied gases (v-DSMC) and the conventional DSMC. Subsequently, a comparison between the convergence behavior of the v-DSMC and analytical data is carried out to scrutinize the validity of the v-DSMC algorithm. This method makes use of a modified collision model of variable hard sphere (VHS) termed Maxwell-VHS, which considers an equal contingency of collision but an arbitrary viscosity variation with temperature, for all adjacent gas particles. The results of the numerical simulation declare the convergence rate of the v-DSMC is noticeably faster than those performed by the conventional DSMC; however, a slight computational error occurs at the same simulation time due to higher accuracy of collision sampling in the conventional DSMC. Moreover, the results show a good agreement between the convergence behaviors of the v-DSMC in comparison with the analytical data.","PeriodicalId":54305,"journal":{"name":"Journal of Computational and Theoretical Transport","volume":"49 1","pages":"103 - 120"},"PeriodicalIF":0.7,"publicationDate":"2020-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/23324309.2020.1770796","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49346754","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-01-30DOI: 10.1080/23324309.2019.1710214
R. S. Jeffers, J. Kópházi, M. D. Eaton, F. Févotte, F. Hülsemann, J. Ragusa
Abstract Goal-based error estimation due to spatial discretization and adaptive mesh refinement (AMR) has previously been investigated for the one dimensional, diamond difference, discrete ordinate (1-D DD-SN) method for discretizing the Neutron Transport Equation (NTE). This paper investigates the challenges of extending goal-based error estimation to multi-dimensions with supporting evidence provided on 2-D fixed (extraneous) source and Keff eigenvalue (criticality) verification test cases. It was found that extending Hennart’s weighted residual view of the lowest order 1-D DD equations to multi-dimensions gave what has previously been called the box method. This paper shows how the box method can be extended to higher orders. The paper also shows an equivalence between the higher order box methods and the higher order DD methods derived by Hébert et al. Though, less information is retained in the final solution in the latter case. These extensions allow for the definition of dual weighted residual (DWR) error estimators in multi-dimensions for the DD and box methods. However, they are not applied to drive AMR in the multi-dimensional case due to the various challenges explained in this paper.
{"title":"Goal-Based Error Estimation for the Multi-Dimensional Diamond Difference and Box Discrete Ordinate (SN) Methods","authors":"R. S. Jeffers, J. Kópházi, M. D. Eaton, F. Févotte, F. Hülsemann, J. Ragusa","doi":"10.1080/23324309.2019.1710214","DOIUrl":"https://doi.org/10.1080/23324309.2019.1710214","url":null,"abstract":"Abstract Goal-based error estimation due to spatial discretization and adaptive mesh refinement (AMR) has previously been investigated for the one dimensional, diamond difference, discrete ordinate (1-D DD-SN) method for discretizing the Neutron Transport Equation (NTE). This paper investigates the challenges of extending goal-based error estimation to multi-dimensions with supporting evidence provided on 2-D fixed (extraneous) source and Keff eigenvalue (criticality) verification test cases. It was found that extending Hennart’s weighted residual view of the lowest order 1-D DD equations to multi-dimensions gave what has previously been called the box method. This paper shows how the box method can be extended to higher orders. The paper also shows an equivalence between the higher order box methods and the higher order DD methods derived by Hébert et al. Though, less information is retained in the final solution in the latter case. These extensions allow for the definition of dual weighted residual (DWR) error estimators in multi-dimensions for the DD and box methods. However, they are not applied to drive AMR in the multi-dimensional case due to the various challenges explained in this paper.","PeriodicalId":54305,"journal":{"name":"Journal of Computational and Theoretical Transport","volume":"49 1","pages":"51 - 87"},"PeriodicalIF":0.7,"publicationDate":"2020-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/23324309.2019.1710214","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47670354","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-01-23DOI: 10.1080/23324309.2019.1709873
Berhanu Aragie
Abstract We study the dynamics of charge carriers jumping from one trap to the other of potential trap depth Φ in a one-dimensional semiconductor layer with the help of thermal noise. Applying a nonuniform temperature, colder around the center and hotter on moving away from it, favors the charge carriers to migrate toward the center and populate around the center. However, exposing the system to another additional nonuniform temperature, hotter around the center, forced the charge carriers to redistribute around two points. The trap potential together with the nonuniform temperature forms a system similar to having bistable potential. Diffusion of charge carriers and thermally transition rate, in a high barrier limit, as a function of controlling parameters has been explored. Due to a time-varying signal the system shows stochastic resonance (SR). The noise that made phase transition also favors the system to exhibit SR by applying a time varying signal. Using two-state approximation, SR of charge carriers diffusion, both analytical and numerical simulation, has been investigated. Our finding shows a strong spectral amplification η at a low temperature.
{"title":"Stochastic Resonance of Charge Carriers Diffusion in a Semiconductor Layer under a Nonuniform Low Temperature","authors":"Berhanu Aragie","doi":"10.1080/23324309.2019.1709873","DOIUrl":"https://doi.org/10.1080/23324309.2019.1709873","url":null,"abstract":"Abstract We study the dynamics of charge carriers jumping from one trap to the other of potential trap depth Φ in a one-dimensional semiconductor layer with the help of thermal noise. Applying a nonuniform temperature, colder around the center and hotter on moving away from it, favors the charge carriers to migrate toward the center and populate around the center. However, exposing the system to another additional nonuniform temperature, hotter around the center, forced the charge carriers to redistribute around two points. The trap potential together with the nonuniform temperature forms a system similar to having bistable potential. Diffusion of charge carriers and thermally transition rate, in a high barrier limit, as a function of controlling parameters has been explored. Due to a time-varying signal the system shows stochastic resonance (SR). The noise that made phase transition also favors the system to exhibit SR by applying a time varying signal. Using two-state approximation, SR of charge carriers diffusion, both analytical and numerical simulation, has been investigated. Our finding shows a strong spectral amplification η at a low temperature.","PeriodicalId":54305,"journal":{"name":"Journal of Computational and Theoretical Transport","volume":"49 1","pages":"102 - 88"},"PeriodicalIF":0.7,"publicationDate":"2020-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/23324309.2019.1709873","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41848973","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-01-16DOI: 10.1080/23324309.2020.1816552
Robert Palmer, R. Vasques
Abstract In nonclassical transport, the free-path length variable s is modeled as an independent variable, and a nonclassical linear Boltzmann transport equation incorporating s has been derived. To model transport in diffusive regimes, the simplified spherical harmonic equations (SPN) have been successfully employed. To model nonclassical transport in diffusive regimes, nonclassical versions of the SPN equations are needed. Nonclassical SPN equations to model isotropic scattering have been derived, and the nonclassical SP1 equation with anisotropic scattering has been determined, but the method used to derive it cannot derive the higher order equations. This article presents a new method which will be able to derive all the nonclassical SPN equations with anisotropic scattering. This method is presented and is used to produce the first of these equations, and it is shown to be equivalent to the previously derived nonclassical SP1 equation with anisotropic scattering.
{"title":"Asymptotic Derivation of the Simplified PN Equations for Nonclassical Transport with Anisotropic Scattering","authors":"Robert Palmer, R. Vasques","doi":"10.1080/23324309.2020.1816552","DOIUrl":"https://doi.org/10.1080/23324309.2020.1816552","url":null,"abstract":"Abstract In nonclassical transport, the free-path length variable s is modeled as an independent variable, and a nonclassical linear Boltzmann transport equation incorporating s has been derived. To model transport in diffusive regimes, the simplified spherical harmonic equations (SPN) have been successfully employed. To model nonclassical transport in diffusive regimes, nonclassical versions of the SPN equations are needed. Nonclassical SPN equations to model isotropic scattering have been derived, and the nonclassical SP1 equation with anisotropic scattering has been determined, but the method used to derive it cannot derive the higher order equations. This article presents a new method which will be able to derive all the nonclassical SPN equations with anisotropic scattering. This method is presented and is used to produce the first of these equations, and it is shown to be equivalent to the previously derived nonclassical SP1 equation with anisotropic scattering.","PeriodicalId":54305,"journal":{"name":"Journal of Computational and Theoretical Transport","volume":"49 1","pages":"331 - 348"},"PeriodicalIF":0.7,"publicationDate":"2020-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/23324309.2020.1816552","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47207933","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-01-02DOI: 10.1080/23324309.2019.1709081
Guanyu Xue, Hui Feng
Abstract In this paper, an alternating segment explicit-implicit (ASE-I) scheme with intrinsic parallelism for Burgers’ equation is proposed. The scheme has second-order truncation error in space and it is linear stable by analysis of the linearization procedure. The ASE-I scheme can be extended to solve two-dimensional Burgers’ equations by alternating direction implicit (ADI) technique. Numerical experiments show the new scheme is efficient and reliable.
{"title":"An Alternating Segment Explicit-Implicit Scheme with Intrinsic Parallelism for Burgers’ Equation","authors":"Guanyu Xue, Hui Feng","doi":"10.1080/23324309.2019.1709081","DOIUrl":"https://doi.org/10.1080/23324309.2019.1709081","url":null,"abstract":"Abstract In this paper, an alternating segment explicit-implicit (ASE-I) scheme with intrinsic parallelism for Burgers’ equation is proposed. The scheme has second-order truncation error in space and it is linear stable by analysis of the linearization procedure. The ASE-I scheme can be extended to solve two-dimensional Burgers’ equations by alternating direction implicit (ADI) technique. Numerical experiments show the new scheme is efficient and reliable.","PeriodicalId":54305,"journal":{"name":"Journal of Computational and Theoretical Transport","volume":"49 1","pages":"15 - 30"},"PeriodicalIF":0.7,"publicationDate":"2020-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/23324309.2019.1709081","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44944263","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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