Alexey Yu. Chernenkov, Evgeny M. Volodin, Victor M. Stepanenko
Nitrogen is one of the most abundant chemical elements on the Earth and plays an important role in global environmental change. Leading Earth system models include coupled carbon and nitrogen cycle modules of varying complexity, but the INM RAS climate model family has not yet included an explicit N-cycle description. This paper presents a parameterization of the terrestrial N-cycle based on a simplification of the JULES-CN model, adapted for coupled use with the INM-CM land C-cycle module. Numerical simulations were carried out with a standalone carbon cycle model with nitrogen feedback disabled and enabled versions for the period 1850–2100. The simulated global pools show good agreement with results of other models with an implemented N-cycle. Taking into account the N-limitation of the C-cycle, the modelled dynamics of total carbon storage in terrestrial ecosystems from 1850 to the mid-20th century is specified.
{"title":"Nitrogen cycle module for INM RAS climate model","authors":"Alexey Yu. Chernenkov, Evgeny M. Volodin, Victor M. Stepanenko","doi":"10.1515/rnam-2024-0018","DOIUrl":"https://doi.org/10.1515/rnam-2024-0018","url":null,"abstract":"Nitrogen is one of the most abundant chemical elements on the Earth and plays an important role in global environmental change. Leading Earth system models include coupled carbon and nitrogen cycle modules of varying complexity, but the INM RAS climate model family has not yet included an explicit N-cycle description. This paper presents a parameterization of the terrestrial N-cycle based on a simplification of the JULES-CN model, adapted for coupled use with the INM-CM land C-cycle module. Numerical simulations were carried out with a standalone carbon cycle model with nitrogen feedback disabled and enabled versions for the period 1850–2100. The simulated global pools show good agreement with results of other models with an implemented N-cycle. Taking into account the N-limitation of the C-cycle, the modelled dynamics of total carbon storage in terrestrial ecosystems from 1850 to the mid-20th century is specified.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141936427","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
SLNE is the coupled model, that was developed in 2023. SL and NE here are the first two letters from SLAV (Semi-Lagrangian, based on Absolute Vorticity equation) model of the atmosphere and NEMO (Nucleus for European Modelling of the Ocean) ocean model that have been coupled using OASIS3-MCT software. The initial conditions for SLAV and NEMO are specified from an atmospheric and ocean analyses produced in Hydrometcentre of Russia. The 2010–2021 hindcast accuracy study shows, that SLNE has comparable errors to the operational SLAV model on a sub-seasonal time scale. The SLNE model has improved prediction skill of the 2010 heatwave features in comparison to SLAV, that is a motivation for further work to improve the coupled model.
{"title":"Evaluation of 2010 heatwave prediction skill by SLNE coupled model","authors":"Rostislav Yu. Fadeev","doi":"10.1515/rnam-2024-0019","DOIUrl":"https://doi.org/10.1515/rnam-2024-0019","url":null,"abstract":"SLNE is the coupled model, that was developed in 2023. SL and NE here are the first two letters from SLAV (Semi-Lagrangian, based on Absolute Vorticity equation) model of the atmosphere and NEMO (Nucleus for European Modelling of the Ocean) ocean model that have been coupled using OASIS3-MCT software. The initial conditions for SLAV and NEMO are specified from an atmospheric and ocean analyses produced in Hydrometcentre of Russia. The 2010–2021 hindcast accuracy study shows, that SLNE has comparable errors to the operational SLAV model on a sub-seasonal time scale. The SLNE model has improved prediction skill of the 2010 heatwave features in comparison to SLAV, that is a motivation for further work to improve the coupled model.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141936429","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Tatyana S. Khachkova, Vadim V. Lisitsa, Elena A. Gondul, Dmiriy I. Prokhorov, Viktor I. Kostin
The paper presents an algorithm for three-dimensional modelling of two-phase flows on the scale of pore size order for numerical evaluation of relative phase permeability curves of porous materials. Such an evaluation is performed based on the results of numerical simulation of primary drainage with subsequent waterflooding. In this case, models of porous materials based on three-dimensional tomographic images of rocks are used. The simulation of the flow considers the Stokes equation and the Cahn–Hilliard equation for modelling phase transfer, which allows us to determine phases using the concentration function. The combination of the phase field method and finite difference method makes it possible to correctly take into account the contact angle and stably calculate surface tension forces in domains with complex topology.
{"title":"Two-phase flow simulation algorithm for numerical estimation of relative phase permeability curves of porous materials","authors":"Tatyana S. Khachkova, Vadim V. Lisitsa, Elena A. Gondul, Dmiriy I. Prokhorov, Viktor I. Kostin","doi":"10.1515/rnam-2024-0020","DOIUrl":"https://doi.org/10.1515/rnam-2024-0020","url":null,"abstract":"The paper presents an algorithm for three-dimensional modelling of two-phase flows on the scale of pore size order for numerical evaluation of relative phase permeability curves of porous materials. Such an evaluation is performed based on the results of numerical simulation of primary drainage with subsequent waterflooding. In this case, models of porous materials based on three-dimensional tomographic images of rocks are used. The simulation of the flow considers the Stokes equation and the Cahn–Hilliard equation for modelling phase transfer, which allows us to determine phases using the concentration function. The combination of the phase field method and finite difference method makes it possible to correctly take into account the contact angle and stably calculate surface tension forces in domains with complex topology.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141936467","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Ivan G. Chechkin, Kirill V. Demyanko, Yuri M. Nechepurenko
An original numerical matrix algorithm aimed at solving the optimal control problems for linear systems of ordinary differential equations with constant coefficients is proposed. The work of the algorithm is demonstrated with the problem, which consists in generating a given small disturbance of the Poiseuille flow in an infinite duct by blowing and suction through the walls. The costs of creating the leading modes and optimal disturbances are compared, which is of independent interest.
{"title":"Numerical solution of optimal control problems for linear systems of ordinary differential equations","authors":"Ivan G. Chechkin, Kirill V. Demyanko, Yuri M. Nechepurenko","doi":"10.1515/rnam-2024-0017","DOIUrl":"https://doi.org/10.1515/rnam-2024-0017","url":null,"abstract":"An original numerical matrix algorithm aimed at solving the optimal control problems for linear systems of ordinary differential equations with constant coefficients is proposed. The work of the algorithm is demonstrated with the problem, which consists in generating a given small disturbance of the Poiseuille flow in an infinite duct by blowing and suction through the walls. The costs of creating the leading modes and optimal disturbances are compared, which is of independent interest.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141936440","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
M. S. Akenteva, N. A. Kargapolova, V. A. Ogorodnikov
In this paper, we present three algorithms for simulation of intervals of stationary vector and scalar sequences with partial distributions of their subsequences of fixed length in the form of a mixture of Gaussian distributions. The first algorithm is based on superposition of two Gaussian vector processes and the second and third ones use the method of conditional distributions and the method of superpositions to simulate the mixtures and to select realizations for approximate construction of conditional realizations. Some properties of these algorithms are presented.
{"title":"Simulation algorithms for stationary sequences with distributions in the form of a mixture of Gaussian distributions","authors":"M. S. Akenteva, N. A. Kargapolova, V. A. Ogorodnikov","doi":"10.1515/rnam-2024-0012","DOIUrl":"https://doi.org/10.1515/rnam-2024-0012","url":null,"abstract":"\u0000 In this paper, we present three algorithms for simulation of intervals of stationary vector and scalar sequences with partial distributions of their subsequences of fixed length in the form of a mixture of Gaussian distributions. The first algorithm is based on superposition of two Gaussian vector processes and the second and third ones use the method of conditional distributions and the method of superpositions to simulate the mixtures and to select realizations for approximate construction of conditional realizations. Some properties of these algorithms are presented.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141280492","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The paper demonstrates two approaches to constructing monotonic difference schemes for the transfer equation in divergent form from the family of semi-Lagrangian methods: Eulerian–Lagrangian and Lagrangian–Eulerian. Within each approach, a monotonic conservative difference scheme is proposed. It is shown that within the framework of the Lagrangian–Eulerian approach, based on the use of curvilinear grids formed by the characteristics of the approximated transfer operator, it is possible to construct monotonic difference schemes of second order accuracy.
{"title":"Semi-Lagrangian approximations of the transfer operator in divergent form","authors":"V. Shaydurov, Viktoriya S. Petrakova","doi":"10.1515/rnam-2024-0015","DOIUrl":"https://doi.org/10.1515/rnam-2024-0015","url":null,"abstract":"\u0000 The paper demonstrates two approaches to constructing monotonic difference schemes for the transfer equation in divergent form from the family of semi-Lagrangian methods: Eulerian–Lagrangian and Lagrangian–Eulerian. Within each approach, a monotonic conservative difference scheme is proposed. It is shown that within the framework of the Lagrangian–Eulerian approach, based on the use of curvilinear grids formed by the characteristics of the approximated transfer operator, it is possible to construct monotonic difference schemes of second order accuracy.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141279709","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The paper deals with an Eulerian model for heterogeneous multiphase (multi-material) elasto-plastic media based on the diffuse interface method in the one-dimensional uniaxial strain approximation. In this approximation, an equilibrium hypoelastic Wilkins bi-material model is derived. This is carried out on the basis of an analogy between the elasto-plastic Wilkins and hydrodynamic Euler models. For the obtained model, a Godunov-type numerical method is developed based on the approximate Riemann solver HLLC. The results of the proposed Eulerian diffuse interface model are compared with reference solutions on moving grids with explicit tracking interfaces. It is shown that the present diffuse interface numerical model describes with good accuracy strong shock-wave processes in heterogeneous multiphase elasto-plastic media.
{"title":"Numerical modelling of large elasto-plastic multi-material deformations on Eulerian grids","authors":"Lujie Wang, I. Menshov, Alexey A. Serezhkin","doi":"10.1515/rnam-2024-0016","DOIUrl":"https://doi.org/10.1515/rnam-2024-0016","url":null,"abstract":"\u0000 The paper deals with an Eulerian model for heterogeneous multiphase (multi-material) elasto-plastic media based on the diffuse interface method in the one-dimensional uniaxial strain approximation. In this approximation, an equilibrium hypoelastic Wilkins bi-material model is derived. This is carried out on the basis of an analogy between the elasto-plastic Wilkins and hydrodynamic Euler models. For the obtained model, a Godunov-type numerical method is developed based on the approximate Riemann solver HLLC. The results of the proposed Eulerian diffuse interface model are compared with reference solutions on moving grids with explicit tracking interfaces. It is shown that the present diffuse interface numerical model describes with good accuracy strong shock-wave processes in heterogeneous multiphase elasto-plastic media.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141279197","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The paper deals with Monte Carlo simulation of polarized radiative transfer and lidar returns in sensing of atmospheric clouds. The Stokes parameters were used to describe the transfer of polarized radiation, and computation of the lidar returns was based on flux-at-point estimators. We consider modifications of the numerical algorithm with scattering according to the phase function for unpolarized light and with scattering depending on polarization. Numerical experiments were performed for lidar sensing of waterdrop clouds.
{"title":"Monte Carlo simulation of polarized lidar returns for atmospheric clouds sensing","authors":"S. Prigarin, Evgenia G. Kablukova, Xue Zhang","doi":"10.1515/rnam-2024-0013","DOIUrl":"https://doi.org/10.1515/rnam-2024-0013","url":null,"abstract":"\u0000 The paper deals with Monte Carlo simulation of polarized radiative transfer and lidar returns in sensing of atmospheric clouds. The Stokes parameters were used to describe the transfer of polarized radiation, and computation of the lidar returns was based on flux-at-point estimators. We consider modifications of the numerical algorithm with scattering according to the phase function for unpolarized light and with scattering depending on polarization. Numerical experiments were performed for lidar sensing of waterdrop clouds.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141282040","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Stochastic simulation algorithm for solving exciton transport in a 3D layered semiconductor heterostructure is developed. The problem is governed by a transient drift-diffusion-recombination equation with Dirichlet and Neumann mixed boundary conditions. The semiconductor is represented as an infinite multilayer of finite thickness along the transverse coordinate z. The multilayer is composed by a set of sublayers of different materials so that the excitons have different diffusion and recombination coefficients in each layer. Continuity of solutions and fluxes at the plane interfaces between layers are imposed. The stochastic simulation algorithm solves the transport problem by tracking exciton trajectories in accordance with the probability distributions represented through the Green function of the problem in each sublayer. The method is meshless, the excitons jump only over the plane boundaries of the layers. This explains the high efficiency of the method. Simulation results for transport problems with different mixed boundary conditions are presented.
{"title":"Stochastic simulation of exciton transport in semiconductor heterostructures","authors":"Karl Sabelfeld, I. Aksyuk","doi":"10.1515/rnam-2024-0014","DOIUrl":"https://doi.org/10.1515/rnam-2024-0014","url":null,"abstract":"\u0000 Stochastic simulation algorithm for solving exciton transport in a 3D layered semiconductor heterostructure is developed. The problem is governed by a transient drift-diffusion-recombination equation with Dirichlet and Neumann mixed boundary conditions. The semiconductor is represented as an infinite multilayer of finite thickness along the transverse coordinate z. The multilayer is composed by a set of sublayers of different materials so that the excitons have different diffusion and recombination coefficients in each layer. Continuity of solutions and fluxes at the plane interfaces between layers are imposed. The stochastic simulation algorithm solves the transport problem by tracking exciton trajectories in accordance with the probability distributions represented through the Green function of the problem in each sublayer. The method is meshless, the excitons jump only over the plane boundaries of the layers. This explains the high efficiency of the method. Simulation results for transport problems with different mixed boundary conditions are presented.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141280099","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We study the accuracy of shock-capturing schemes for the shallow water Cauchy problems with piecewise smooth discontinuous initial data. We consider the second order balance-characteristic (CABARETM) scheme, the third order finite-difference Rusanov–Burstein–Mirin (RBM) scheme and the fifth order in space, the third order in time weighted essentially non-oscillatory (WENO5) scheme. We have shown that the maximum loss of accuracy occurs in the centered rarefaction waves of the exact solutions, where all these schemes have the first order of convergence and fairly close values of the numerical disbalances (errors), regardless of their formal approximation order on the smooth solutions. In the same time, inside the shock influence areas the considered schemes can have different convergence orders and, as a result, significantly different accuracy. In particular, when solving the Cauchy problem with periodic initial data, when the exact solution has no centered rarefaction waves, the RBM scheme has a significantly higher accuracy inside the shock influence areas, compared to the CABARETM and WENO5 schemes. It means that the combined scheme, in which the RBM scheme is a basic scheme and the CABARETM scheme is an internal one, can be effectively used to compute weak solutions of such type Cauchy problems.
{"title":"On the accuracy of shock-capturing schemes when calculating Cauchy problems with periodic discontinuous initial data","authors":"Olyana A. Kovyrkina, Vladimir V. Ostapenko","doi":"10.1515/rnam-2024-0009","DOIUrl":"https://doi.org/10.1515/rnam-2024-0009","url":null,"abstract":"We study the accuracy of shock-capturing schemes for the shallow water Cauchy problems with piecewise smooth discontinuous initial data. We consider the second order balance-characteristic (CABARETM) scheme, the third order finite-difference Rusanov–Burstein–Mirin (RBM) scheme and the fifth order in space, the third order in time weighted essentially non-oscillatory (WENO5) scheme. We have shown that the maximum loss of accuracy occurs in the centered rarefaction waves of the exact solutions, where all these schemes have the first order of convergence and fairly close values of the numerical disbalances (errors), regardless of their formal approximation order on the smooth solutions. In the same time, inside the shock influence areas the considered schemes can have different convergence orders and, as a result, significantly different accuracy. In particular, when solving the Cauchy problem with periodic initial data, when the exact solution has no centered rarefaction waves, the RBM scheme has a significantly higher accuracy inside the shock influence areas, compared to the CABARETM and WENO5 schemes. It means that the combined scheme, in which the RBM scheme is a basic scheme and the CABARETM scheme is an internal one, can be effectively used to compute weak solutions of such type Cauchy problems.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140560495","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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