Pub Date : 2025-03-04DOI: 10.1016/j.cpc.2025.109574
Marco Neri , Pasquale Zumbolo , Raffaele Albanese
This paper presents a novel method for accurately tracing magnetic field lines. This procedure is of particular interest for axisymmetric nuclear fusion devices. The design of the plasma facing components in a tokamak strictly depends on the Scrape-Off Layer (SOL), a thin region of open field lines through which charged particles and energy flow out from the plasma core to the solid walls with a huge heat flux. The power exhaust issue is among the top priorities in the European Fusion Roadmap, hence the determination of the plasma boundary and SOL with a high accuracy is essential. Existing equilibrium codes using finite element formulations with linear triangles of mesh size provide a piecewise constant magnetic flux gradient, resulting in coarse accuracy of the field lines in the SOL, with an error of order , especially near the X-point where the flux gradient approaches zero. The proposed procedure is based on a method introduced in 2023, which achieves continuity and a convergence rate of order for the magnetic flux gradient too. The magnetic poloidal flux is then approximated with a piecewise polynomial function of second or third degree in the triangles. A more accurate evaluation of the plasma boundary and SOL field lines is obtained, particularly near the X-point, which is no longer constrained to be a mesh node. The method has been successfully tested in two cases with available analytical solutions. It has also been used as a post-processor for the flat top configuration of the DTT tokamak obtained with the free boundary CREATE-NL+ equilibrium code. For a given accuracy, the computational cost of the procedure is significantly lower than alternative methods relying on finer first order discretization or techniques using triangular C1 finite elements.
{"title":"Accurate plasma boundary calculation using linear triangular finite elements","authors":"Marco Neri , Pasquale Zumbolo , Raffaele Albanese","doi":"10.1016/j.cpc.2025.109574","DOIUrl":"10.1016/j.cpc.2025.109574","url":null,"abstract":"<div><div>This paper presents a novel method for accurately tracing magnetic field lines. This procedure is of particular interest for axisymmetric nuclear fusion devices. The design of the plasma facing components in a tokamak strictly depends on the Scrape-Off Layer (SOL), a thin region of open field lines through which charged particles and energy flow out from the plasma core to the solid walls with a huge heat flux. The power exhaust issue is among the top priorities in the European Fusion Roadmap, hence the determination of the plasma boundary and SOL with a high accuracy is essential. Existing equilibrium codes using finite element formulations with linear triangles of mesh size <span><math><mi>h</mi></math></span> provide a piecewise constant magnetic flux gradient, resulting in coarse accuracy of the field lines in the SOL, with an error of order <span><math><mrow><mi>O</mi><mo>(</mo><mi>h</mi><mo>)</mo></mrow></math></span>, especially near the X-point where the flux gradient approaches zero. The proposed procedure is based on a method introduced in 2023, which achieves continuity and a convergence rate of order <span><math><mrow><mi>O</mi><mo>(</mo><msup><mrow><mi>h</mi></mrow><mn>2</mn></msup><mo>)</mo><mspace></mspace></mrow></math></span> for the magnetic flux gradient too. The magnetic poloidal flux is then approximated with a piecewise polynomial function of second or third degree in the triangles. A more accurate evaluation of the plasma boundary and SOL field lines is obtained, particularly near the X-point, which is no longer constrained to be a mesh node. The method has been successfully tested in two cases with available analytical solutions. It has also been used as a post-processor for the flat top configuration of the DTT tokamak obtained with the free boundary CREATE-NL+ equilibrium code. For a given accuracy, the computational cost of the procedure is significantly lower than alternative methods relying on finer first order discretization or techniques using triangular C<sup>1</sup> finite elements.</div></div>","PeriodicalId":285,"journal":{"name":"Computer Physics Communications","volume":"311 ","pages":"Article 109574"},"PeriodicalIF":7.2,"publicationDate":"2025-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143611268","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-03-04DOI: 10.1016/j.cpc.2025.109573
N. Stanojević , A. Demić , N. Vuković , P. Dean , Z. Ikonić , D. Indjin , J. Radovanović
We develop a machine precision transfer matrix method that can be used for a wide range of ordinary differential equations and eigenvalue problems. One of the major drawbacks of transfer matrix approaches is the requirement to sweep parameters in a shooting-like manner, thus lacking in precision in comparison to finite difference methods. We resolve this by finding the zero of the analytically calculated first derivative of the transfer matrix. This allows us to outperform the finite difference approach and compute eigenvalues with high precision and linear numerical complexity. We test the developed model in the following scenarios in semiconductor quantum heterostructures: standard Schrödinger equation under effective mass approximation with parabolic subbands, with two-band nonparabolicity, a order Schrödigner equation that accounts for nonparabolic subbands using the 14 k⋅p approach and calculation of the interface phonon modes dispersion relations and the mode profiles. We show that the developed derivative transfer matrix method outperforms the finite difference method by being able to handle higher spatial resolution and having better time performance. The numerical implementation of our models is available as an open-source package in MATLAB version that can be found on https://github.com/AcaDemicNanoLab/dTMM_Schrodinger.
{"title":"Derivative transfer matrix method: Machine precision calculation of electron structure and interface phonon dispersion in semiconductor heterostructures","authors":"N. Stanojević , A. Demić , N. Vuković , P. Dean , Z. Ikonić , D. Indjin , J. Radovanović","doi":"10.1016/j.cpc.2025.109573","DOIUrl":"10.1016/j.cpc.2025.109573","url":null,"abstract":"<div><div>We develop a machine precision transfer matrix method that can be used for a wide range of ordinary differential equations and eigenvalue problems. One of the major drawbacks of transfer matrix approaches is the requirement to sweep parameters in a shooting-like manner, thus lacking in precision in comparison to finite difference methods. We resolve this by finding the zero of the analytically calculated first derivative of the transfer matrix. This allows us to outperform the finite difference approach and compute eigenvalues with high precision and linear numerical complexity. We test the developed model in the following scenarios in semiconductor quantum heterostructures: standard Schrödinger equation under effective mass approximation with parabolic subbands, with two-band nonparabolicity, a <span><math><msup><mrow><mn>4</mn></mrow><mrow><mi>th</mi></mrow></msup></math></span> order Schrödigner equation that accounts for nonparabolic subbands using the 14 <strong>k</strong>⋅<strong>p</strong> approach and calculation of the interface phonon modes dispersion relations and the mode profiles. We show that the developed derivative transfer matrix method outperforms the finite difference method by being able to handle higher spatial resolution and having better time performance. The numerical implementation of our models is available as an open-source package in MATLAB version that can be found on <span><span>https://github.com/AcaDemicNanoLab/dTMM_Schrodinger</span><svg><path></path></svg></span>.</div></div>","PeriodicalId":285,"journal":{"name":"Computer Physics Communications","volume":"311 ","pages":"Article 109573"},"PeriodicalIF":7.2,"publicationDate":"2025-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143601118","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-03-04DOI: 10.1016/j.cpc.2025.109571
Fenglian Zheng, Xufeng Xiao
The growth phenomenon of dendritic crystals is a common occurrence in nature, forming a structure similar to tree branches during its evolution. However, in practical computations, model parameters and initial conditions may have observational errors, which cause large errors in numerical simulation results. To improve the accuracy and efficiency of numerical simulation, this study uses a three-dimensional variational (3DVar) data assimilation algorithm. We consider using the phase-field dendritic crystal growth (PF-DCG) model as the governing equation for numerical simulation. Through the optimization problem of 3DVar, we will incorporate the observed solutions from experimental data into the process of solving numerical solutions to modify them, thereby achieving the goal of data assimilation. This study mainly evaluates two different categories of problems: initial observational errors and model parameter errors. In the numerical experiment section, we obtain the numerical solution by using the operator splitting method (OSM) and explore the effectiveness of this method and investigate the influence of various factors such as adjustment factors, spatio-temporal sampling rates, and parameter perturbation ratios on the effectiveness of data assimilation. The experimental results show that this method can effectively assimilate the observation data, thus accurately simulating the growth process of dendritic crystals.
{"title":"Accurate simulation of the anisotropic dendrite crystal growth by the 3DVar data assimilation","authors":"Fenglian Zheng, Xufeng Xiao","doi":"10.1016/j.cpc.2025.109571","DOIUrl":"10.1016/j.cpc.2025.109571","url":null,"abstract":"<div><div>The growth phenomenon of dendritic crystals is a common occurrence in nature, forming a structure similar to tree branches during its evolution. However, in practical computations, model parameters and initial conditions may have observational errors, which cause large errors in numerical simulation results. To improve the accuracy and efficiency of numerical simulation, this study uses a three-dimensional variational (3DVar) data assimilation algorithm. We consider using the phase-field dendritic crystal growth (PF-DCG) model as the governing equation for numerical simulation. Through the optimization problem of 3DVar, we will incorporate the observed solutions from experimental data into the process of solving numerical solutions to modify them, thereby achieving the goal of data assimilation. This study mainly evaluates two different categories of problems: initial observational errors and model parameter errors. In the numerical experiment section, we obtain the numerical solution by using the operator splitting method (OSM) and explore the effectiveness of this method and investigate the influence of various factors such as adjustment factors, spatio-temporal sampling rates, and parameter perturbation ratios on the effectiveness of data assimilation. The experimental results show that this method can effectively assimilate the observation data, thus accurately simulating the growth process of dendritic crystals.</div></div>","PeriodicalId":285,"journal":{"name":"Computer Physics Communications","volume":"311 ","pages":"Article 109571"},"PeriodicalIF":7.2,"publicationDate":"2025-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143552982","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-03-03DOI: 10.1016/j.cpc.2025.109570
Andrei Ludvig-Osipov , Dmytro Yadykin , Pär Strand
An efficient numerical scheme for solving transport equations for tokamak plasmas within an integrated modelling framework is presented. The plasma transport equations are formulated as diffusion-advection equations in two coordinates (one temporal and one spatial) featuring stiff non-linearities. The presented numerical scheme aims to minimise computational costs, which are associated with repeated calls of numerically expensive physical models in a processes of time stepping and non-linear convergence within an integrated modelling framework. The spatial discretisation is based on the 4th order accurate Interpolated Differential Operator in Conservative Formulation, the time-stepping method is the 2nd order accurate implicit Runge-Kutta scheme, and an under-relaxed Picard iteration is used for accelerating non-linear convergence. Temporal and spatial accuracies of the scheme allow for coarse grids, and the implicit time-stepping method together with the non-linear convergence approach contributes to robust and fast non-linear convergence. The spatial discretisation method enforces conservation in spatial coordinate up to the machine precision. The numerical scheme demonstrates accurate, stable and fast non-linear convergence in numerical tests using analytical stiff transport model. In particular, the 2nd order accuracy in time stepping significantly improves the overall convergence properties and the accuracy of simulating transient processes in comparison to the 1st order schemes.
{"title":"High-order implicit solver in conservative formulation for tokamak plasma transport equations","authors":"Andrei Ludvig-Osipov , Dmytro Yadykin , Pär Strand","doi":"10.1016/j.cpc.2025.109570","DOIUrl":"10.1016/j.cpc.2025.109570","url":null,"abstract":"<div><div>An efficient numerical scheme for solving transport equations for tokamak plasmas within an integrated modelling framework is presented. The plasma transport equations are formulated as diffusion-advection equations in two coordinates (one temporal and one spatial) featuring stiff non-linearities. The presented numerical scheme aims to minimise computational costs, which are associated with repeated calls of numerically expensive physical models in a processes of time stepping and non-linear convergence within an integrated modelling framework. The spatial discretisation is based on the 4th order accurate Interpolated Differential Operator in Conservative Formulation, the time-stepping method is the 2nd order accurate implicit Runge-Kutta scheme, and an under-relaxed Picard iteration is used for accelerating non-linear convergence. Temporal and spatial accuracies of the scheme allow for coarse grids, and the implicit time-stepping method together with the non-linear convergence approach contributes to robust and fast non-linear convergence. The spatial discretisation method enforces conservation in spatial coordinate up to the machine precision. The numerical scheme demonstrates accurate, stable and fast non-linear convergence in numerical tests using analytical stiff transport model. In particular, the 2nd order accuracy in time stepping significantly improves the overall convergence properties and the accuracy of simulating transient processes in comparison to the 1st order schemes.</div></div>","PeriodicalId":285,"journal":{"name":"Computer Physics Communications","volume":"311 ","pages":"Article 109570"},"PeriodicalIF":7.2,"publicationDate":"2025-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143552981","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-02-28DOI: 10.1016/j.cpc.2025.109567
Freddie D. Witherden , Peter E. Vincent , Will Trojak , Yoshiaki Abe , Amir Akbarzadeh , Semih Akkurt , Mohammad Alhawwary , Lidia Caros , Tarik Dzanic , Giorgio Giangaspero , Arvind S. Iyer , Antony Jameson , Marius Koch , Niki Loppi , Sambit Mishra , Rishit Modi , Gonzalo Sáez-Mischlich , Jin Seok Park , Brian C. Vermeire , Lai Wang
PyFR is an open-source cross-platform computational fluid dynamics framework based on the high-order Flux Reconstruction approach, specifically designed for undertaking high-accuracy scale-resolving simulations in the vicinity of complex engineering geometries. Since the initial release of PyFR v0.1.0 in 2013, a range of new capabilities have been added to the framework, with a view to enabling industrial adoption. In this work, we provide details of these enhancements as released in PyFR v2.0.3, including improvements to cross-platform performance (new backends, extensions of the DSL, new matrix multiplication providers, improvements to the data layout, use of task graphs) and improvements to numerical stability (modal filtering, anti-aliasing, artificial viscosity, entropy filtering), as well as the addition of prismatic, tetrahedral and pyramid shaped elements, improved domain decomposition support for mixed element grids, improved handling of curved element meshes, the addition of an adaptive time-stepping capability, the addition of incompressible Euler and Navier-Stokes solvers, improvements to file formats and the development of a plugin architecture. We also explain efforts to grow an engaged developer and user community and provided a range of examples that show how our user base is applying PyFR to solve a wide range of fundamental, applied and industrial flow problems. Finally, we demonstrate the accuracy of PyFR v2.0.3 for a supersonic Taylor-Green vortex case, with shocks and turbulence, and provided latest performance and scaling results on up to 1024 AMD Instinct MI250X accelerators of Frontier at ORNL (each with two GCDs) and up to 2048 Nvidia GH200 GPUs of Alps at CSCS. We note that absolute performance of PyFR accounting for the totality of both hardware and software improvements has, conservatively, increased by almost 50× over the last decade.
Program summary
Program Title: PyFR
CPC Library link to program files:https://doi.org/10.17632/vmgh4kfjk6.1
Nature of problem: Accurate and efficient scale-resolving simulation of industrial flows.
Solution method: Massively parallel cross-platform implementation of high-order accurate Flux Reconstruction schemes.
{"title":"PyFR v2.0.3: Towards industrial adoption of scale-resolving simulations","authors":"Freddie D. Witherden , Peter E. Vincent , Will Trojak , Yoshiaki Abe , Amir Akbarzadeh , Semih Akkurt , Mohammad Alhawwary , Lidia Caros , Tarik Dzanic , Giorgio Giangaspero , Arvind S. Iyer , Antony Jameson , Marius Koch , Niki Loppi , Sambit Mishra , Rishit Modi , Gonzalo Sáez-Mischlich , Jin Seok Park , Brian C. Vermeire , Lai Wang","doi":"10.1016/j.cpc.2025.109567","DOIUrl":"10.1016/j.cpc.2025.109567","url":null,"abstract":"<div><div>PyFR is an open-source cross-platform computational fluid dynamics framework based on the high-order Flux Reconstruction approach, specifically designed for undertaking high-accuracy scale-resolving simulations in the vicinity of complex engineering geometries. Since the initial release of PyFR v0.1.0 in 2013, a range of new capabilities have been added to the framework, with a view to enabling industrial adoption. In this work, we provide details of these enhancements as released in PyFR v2.0.3, including improvements to cross-platform performance (new backends, extensions of the DSL, new matrix multiplication providers, improvements to the data layout, use of task graphs) and improvements to numerical stability (modal filtering, anti-aliasing, artificial viscosity, entropy filtering), as well as the addition of prismatic, tetrahedral and pyramid shaped elements, improved domain decomposition support for mixed element grids, improved handling of curved element meshes, the addition of an adaptive time-stepping capability, the addition of incompressible Euler and Navier-Stokes solvers, improvements to file formats and the development of a plugin architecture. We also explain efforts to grow an engaged developer and user community and provided a range of examples that show how our user base is applying PyFR to solve a wide range of fundamental, applied and industrial flow problems. Finally, we demonstrate the accuracy of PyFR v2.0.3 for a supersonic Taylor-Green vortex case, with shocks and turbulence, and provided latest performance and scaling results on up to 1024 AMD Instinct MI250X accelerators of Frontier at ORNL (each with two GCDs) and up to 2048 Nvidia GH200 GPUs of Alps at CSCS. We note that absolute performance of PyFR accounting for the totality of both hardware and software improvements has, conservatively, increased by almost 50× over the last decade.</div></div><div><h3>Program summary</h3><div><em>Program Title:</em> PyFR</div><div><em>CPC Library link to program files:</em> <span><span>https://doi.org/10.17632/vmgh4kfjk6.1</span><svg><path></path></svg></span></div><div><em>Developer's repository link:</em> <span><span>https://github.com/PyFR/PyFR</span><svg><path></path></svg></span></div><div><em>Licensing provisions:</em> BSD 3-clause</div><div><em>Programming language:</em> Python (generating C/OpenMP, CUDA, OpenCL, HIP, Metal)</div><div><em>Nature of problem:</em> Accurate and efficient scale-resolving simulation of industrial flows.</div><div><em>Solution method:</em> Massively parallel cross-platform implementation of high-order accurate Flux Reconstruction schemes.</div></div>","PeriodicalId":285,"journal":{"name":"Computer Physics Communications","volume":"311 ","pages":"Article 109567"},"PeriodicalIF":7.2,"publicationDate":"2025-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143529229","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-02-28DOI: 10.1016/j.cpc.2025.109566
Yash Kumar , Tushar , Souvik Chakraborty
State estimation is imperative while dealing with high-dimensional dynamical systems due to the unavailability of complete measurements. It plays a pivotal role in gaining insights, executing control, or optimizing design tasks. However, many deep learning approaches are constrained by the requirement for high-resolution labels and fixed sensor locations, limiting their practical applicability. To address these limitations, we propose a novel approach featuring an implicit optimization layer and a physics-based loss function capable of learning from sparse labels. This approach operates by minimizing the energy of neural network predictions, thereby accommodating varying sensor counts and locations. Our methodology is validated through the application of these models to two high-dimensional fluid problems: Burgers' equation and Flow Past Cylinder. Notably, our model exhibits robustness against noise in measurements, underscoring its effectiveness in practical scenarios.
{"title":"Energy network for state estimation with random sensors and sparse labels","authors":"Yash Kumar , Tushar , Souvik Chakraborty","doi":"10.1016/j.cpc.2025.109566","DOIUrl":"10.1016/j.cpc.2025.109566","url":null,"abstract":"<div><div>State estimation is imperative while dealing with high-dimensional dynamical systems due to the unavailability of complete measurements. It plays a pivotal role in gaining insights, executing control, or optimizing design tasks. However, many deep learning approaches are constrained by the requirement for high-resolution labels and fixed sensor locations, limiting their practical applicability. To address these limitations, we propose a novel approach featuring an implicit optimization layer and a physics-based loss function capable of learning from sparse labels. This approach operates by minimizing the energy of neural network predictions, thereby accommodating varying sensor counts and locations. Our methodology is validated through the application of these models to two high-dimensional fluid problems: Burgers' equation and Flow Past Cylinder. Notably, our model exhibits robustness against noise in measurements, underscoring its effectiveness in practical scenarios.</div></div>","PeriodicalId":285,"journal":{"name":"Computer Physics Communications","volume":"311 ","pages":"Article 109566"},"PeriodicalIF":7.2,"publicationDate":"2025-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143552984","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-02-26DOI: 10.1016/j.cpc.2025.109564
Akira SaiToh
Recent improvements in the ZKCM and ZKCM_QC libraries are presented in this announcement. ZKCM was released as a C++ library for multiprecision matrix computation and ZKCM_QC was developed as its extension for matrix-product-state (MPS) simulation of quantum circuits. Their parallel processing extensions using OpenMP and CUDA were briefly reported in a previous contribution [A. SaiToh, to appear in Proc. CCP2023]. Here, their most recent developments are reported, which include the employments of advanced FFT and Moore-Penrose inverse routines.
{"title":"New version of ZKCM, a C++ multiprecision matrix library usable for numerical studies of quantum information","authors":"Akira SaiToh","doi":"10.1016/j.cpc.2025.109564","DOIUrl":"10.1016/j.cpc.2025.109564","url":null,"abstract":"<div><div>Recent improvements in the ZKCM and ZKCM_QC libraries are presented in this announcement. ZKCM was released as a C++ library for multiprecision matrix computation and ZKCM_QC was developed as its extension for matrix-product-state (MPS) simulation of quantum circuits. Their parallel processing extensions using OpenMP and CUDA were briefly reported in a previous contribution [A. SaiToh, to appear in Proc. CCP2023]. Here, their most recent developments are reported, which include the employments of advanced FFT and Moore-Penrose inverse routines.</div></div>","PeriodicalId":285,"journal":{"name":"Computer Physics Communications","volume":"311 ","pages":"Article 109564"},"PeriodicalIF":7.2,"publicationDate":"2025-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143508993","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-02-26DOI: 10.1016/j.cpc.2025.109565
Lisong Shi , Chaoxiong Zhang , Chih-Yung Wen
This study introduces the development of space-time Conservation Element and Solution Element (CESE) methods tailored for adaptive unstructured quadrilateral meshes. An efficient algorithm is then proposed to manage the mesh adaptation process for these staggered schemes, utilizing a unique cell-tree-vertex data structure. This structure accelerates the construction of conservation elements and simplifies the interconnection of computational cells, enabling a flexible approach for handling adaptive mesh refinement in complex computational domains. The integration of second-order a-α, Courant number-insensitive, and upwind CESE schemes with this adaptation algorithm is demonstrated. Numerical simulations of compressible inviscid flows are conducted to validate the global conservation property, ensure second-order accuracy across interfaces at different refinement levels, and evaluate the effectiveness of the extended schemes and adaptation algorithm.
{"title":"Adaptive mesh refinement algorithm for CESE schemes on unstructured quadrilateral meshes","authors":"Lisong Shi , Chaoxiong Zhang , Chih-Yung Wen","doi":"10.1016/j.cpc.2025.109565","DOIUrl":"10.1016/j.cpc.2025.109565","url":null,"abstract":"<div><div>This study introduces the development of space-time Conservation Element and Solution Element (CESE) methods tailored for adaptive unstructured quadrilateral meshes. An efficient algorithm is then proposed to manage the mesh adaptation process for these staggered schemes, utilizing a unique cell-tree-vertex data structure. This structure accelerates the construction of conservation elements and simplifies the interconnection of computational cells, enabling a flexible approach for handling adaptive mesh refinement in complex computational domains. The integration of second-order <em>a</em>-<em>α</em>, Courant number-insensitive, and upwind CESE schemes with this adaptation algorithm is demonstrated. Numerical simulations of compressible inviscid flows are conducted to validate the global conservation property, ensure second-order accuracy across interfaces at different refinement levels, and evaluate the effectiveness of the extended schemes and adaptation algorithm.</div></div>","PeriodicalId":285,"journal":{"name":"Computer Physics Communications","volume":"311 ","pages":"Article 109565"},"PeriodicalIF":7.2,"publicationDate":"2025-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143511373","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-02-25DOI: 10.1016/j.cpc.2025.109560
S. Lauterbach, S. Fasoulas, M. Pfeiffer
The gas-surface interaction model of the open-source gas and plasma simulation tool PICLas has been extended for the simulation of catalytic reactions. A variety of reaction mechanisms have been implemented, including multiple adsorption models, desorption, the Eley-Rideal and the Langmuir-Hinshelwood mechanism. Modeling is based upon macroscopic reaction data and parameters derived from experiments or ab-initio quantum calculations. The implementation has been validated through a comparison to analytical reaction rates. Simulations of the carbon monoxide and oxygen reaction network on a Pd(111) surface are performed and compared to experimental data obtained by temperature-programmed desorption spectra and molecular beam measurements. The results show good agreement with the measurement data.
{"title":"Modeling of heterogeneous catalytic reactions with the simulation tool PICLas","authors":"S. Lauterbach, S. Fasoulas, M. Pfeiffer","doi":"10.1016/j.cpc.2025.109560","DOIUrl":"10.1016/j.cpc.2025.109560","url":null,"abstract":"<div><div>The gas-surface interaction model of the open-source gas and plasma simulation tool PICLas has been extended for the simulation of catalytic reactions. A variety of reaction mechanisms have been implemented, including multiple adsorption models, desorption, the Eley-Rideal and the Langmuir-Hinshelwood mechanism. Modeling is based upon macroscopic reaction data and parameters derived from experiments or ab-initio quantum calculations. The implementation has been validated through a comparison to analytical reaction rates. Simulations of the carbon monoxide and oxygen reaction network on a Pd(111) surface are performed and compared to experimental data obtained by temperature-programmed desorption spectra and molecular beam measurements. The results show good agreement with the measurement data.</div></div>","PeriodicalId":285,"journal":{"name":"Computer Physics Communications","volume":"311 ","pages":"Article 109560"},"PeriodicalIF":7.2,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143511374","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-02-25DOI: 10.1016/j.cpc.2025.109563
Ziwei Chai, Sandra Luber
In the self-consistent continuum solvation (SCCS) approach (J. Chem. Phys. 136, 064102 (2012)), the analytical expressions of the local solute-solvent interface functions determine the interface function and dielectric function values at a given real space position based solely on the electron density at that position, completely disregarding the surrounding electron density distribution. Therefore, the low electron density areas inside the solute will be identified by the algorithm as regions where implicit solvent exists, resulting in the emergence of non-physical implicit solvent regions within the solute and even potentially leading to the divergence catastrophe of Kohn-Sham SCF calculations. We present a new and efficient SCCS implementation based on the solvent-aware interface (J. Chem. Theory Comput. 15, 3, 1996–2009 (2019)) which addresses this issue by utilizing a solute-solvent interface function based on convolution of electron density in the CP2K software package, which is based on the mixed Gaussian and plane waves (GPW) approach. Starting with the foundational formulas of SCCS, we have rigorously derived the contributions of the newly defined electrostatic energy to the Kohn-Sham potential and the analytical forces. This comprehensive derivation, which to the best of our knowledge is not available in the current literature, utilizes the updated versions of the solute-solvent interface function and the dielectric function, tailored to align with the specifics of the GPW implementation. Our implementation has been tested to successfully eliminate non-physical implicit solvent regions within the solute and achieve good SCF convergence, as demonstrated by test results for both bulk and surface models, namely liquid H2O, titanium dioxide, and platinum.
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