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Foreword; Preface; Contents; Part I Numerical Methods for Meteorological Problems; 1 On a Conservative Finite-Difference Method for 1D Shallow Water Flows Based on Regularized Equations; 1.1 Introduction; 1.2 The 1d Shallow Water System of Equations, Its Regularization and Discretization; 1.3 Numerical Results; References; 2 Discretization in Numerical Weather Prediction: A Modular Approach to Investigate Spectraland Local SISL Methods; 2.1 Introduction; 2.2 Discretization of the Dynamical Core in NWP; 2.2.1 Time Discretization of the Dynamical Core
2.2.2 Space Discretization of the Dynamical Core and Grids2.3 Spectral SISL Discretization Schemes; 2.4 Study of Local SISL Z-Grid Schemes; 2.4.1 The Z-Grid Approach; 2.4.2 Geostrophic Adjustment of Z-Grid Schemes; 2.4.3 SISL Z-Grid Schemes; 2.4.4 Computational Aspects; 2.5 Conclusion and Outlook; References; 3 Turbulence Modeling Using Fractional Derivatives; 3.1 Introduction; 3.2 Preliminaries; 3.3 Results; 3.3.1 The Fractional Newton's Law of Viscosity; 3.3.2 The Algorithm; 3.3.3 The Test Problem; 3.4 Conclusion; Appendix; References
4 A Parallel Numerical Solution Approach for Nonlinear Parabolic Systems Arising in Air Pollution Transport Problems4.1 Introduction; 4.2 The Numerical Solution Process and its Convergence; 4.2.1 Time Discretization; 4.2.2 FEM Discretization in Space; 4.2.3 Outer Iteration: Damped Newton's Method; 4.2.4 Inner Iteration: Preconditioned CG Method Using Equivalent Operator Preconditioning; 4.3 Some Examples in Air Pollution Models; References; Part II Air Quality Modelling; 5 Eulerian and Lagrangian Approaches for Modellingof Air Quality; 5.1 Introduction; 5.2 Eulerian Models
5.3 Lagrangian Models5.3.1 Puff Models; 5.3.2 Trajectory Models; 5.4 Conclusion; References; 6 Hydrodynamic Modeling of Industrial Pollutants Spreading in Atmosphere; 6.1 Introduction; 6.2 General Hydrodynamic Model of Air Circulation; 6.3 A Model of Turbulence; 6.4 A Model of Cloud and Precipitation; 6.5 Numerical Method for Solving the Non-stationary Problem with a Prehistory Based on Interpolation with Multiple Nodes; 6.6 Interpolating Functions, Specified in Macro-Scale Grid Nodes, into the Meso-Scale Grid; 6.7 Approximation of Constituent Members of the Convection-Diffusion
6.8 Solution of the Problem of Impurities Dispersion in the "Near Field"6.9 Conclusion; References; 7 Coordinate Transformation Approach for Numerical Solution of Environmental Problems; 7.1 Introduction; 7.2 A Stationary Model of Air Pollution; 7.3 A Non-stationary Two-Dimensional Problem; 7.4 Positive Splitting Numerical method; 7.5 Conclusions; References; 8 Impact of Climatic Changes on Pollution Levels; 8.1 Introduction; 8.2 Development of Three Climatic Scenarios ; 8.2.1 Climate Scenario 1 (Taking into Account Only the Future Changes of the Temperatures)
2.2.2 Space Discretization of the Dynamical Core and Grids2.3 Spectral SISL Discretization Schemes; 2.4 Study of Local SISL Z-Grid Schemes; 2.4.1 The Z-Grid Approach; 2.4.2 Geostrophic Adjustment of Z-Grid Schemes; 2.4.3 SISL Z-Grid Schemes; 2.4.4 Computational Aspects; 2.5 Conclusion and Outlook; References; 3 Turbulence Modeling Using Fractional Derivatives; 3.1 Introduction; 3.2 Preliminaries; 3.3 Results; 3.3.1 The Fractional Newton's Law of Viscosity; 3.3.2 The Algorithm; 3.3.3 The Test Problem; 3.4 Conclusion; Appendix; References
4 A Parallel Numerical Solution Approach for Nonlinear Parabolic Systems Arising in Air Pollution Transport Problems4.1 Introduction; 4.2 The Numerical Solution Process and its Convergence; 4.2.1 Time Discretization; 4.2.2 FEM Discretization in Space; 4.2.3 Outer Iteration: Damped Newton's Method; 4.2.4 Inner Iteration: Preconditioned CG Method Using Equivalent Operator Preconditioning; 4.3 Some Examples in Air Pollution Models; References; Part II Air Quality Modelling; 5 Eulerian and Lagrangian Approaches for Modellingof Air Quality; 5.1 Introduction; 5.2 Eulerian Models
5.3 Lagrangian Models5.3.1 Puff Models; 5.3.2 Trajectory Models; 5.4 Conclusion; References; 6 Hydrodynamic Modeling of Industrial Pollutants Spreading in Atmosphere; 6.1 Introduction; 6.2 General Hydrodynamic Model of Air Circulation; 6.3 A Model of Turbulence; 6.4 A Model of Cloud and Precipitation; 6.5 Numerical Method for Solving the Non-stationary Problem with a Prehistory Based on Interpolation with Multiple Nodes; 6.6 Interpolating Functions, Specified in Macro-Scale Grid Nodes, into the Meso-Scale Grid; 6.7 Approximation of Constituent Members of the Convection-Diffusion
6.8 Solution of the Problem of Impurities Dispersion in the "Near Field"6.9 Conclusion; References; 7 Coordinate Transformation Approach for Numerical Solution of Environmental Problems; 7.1 Introduction; 7.2 A Stationary Model of Air Pollution; 7.3 A Non-stationary Two-Dimensional Problem; 7.4 Positive Splitting Numerical method; 7.5 Conclusions; References; 8 Impact of Climatic Changes on Pollution Levels; 8.1 Introduction; 8.2 Development of Three Climatic Scenarios ; 8.2.1 Climate Scenario 1 (Taking into Account Only the Future Changes of the Temperatures)