Uncertainty quantification for hyperbolic and kinetic equations /
نام عام مواد
[Book]
نام نخستين پديدآور
Shi Jin, Lorenzo Pareschi, editors.
وضعیت نشر و پخش و غیره
محل نشرو پخش و غیره
Cham, Switzerland :
نام ناشر، پخش کننده و غيره
Springer,
تاریخ نشرو بخش و غیره
[2018]
مشخصات ظاهری
نام خاص و کميت اثر
1 online resource :
ساير جزييات
illustrations (some color)
فروست
عنوان فروست
SEMA SIMAI Springer series,
مشخصه جلد
volume 14
شاپا ي ISSN فروست
2199-305X ;
یادداشتهای مربوط به کتابنامه ، واژه نامه و نمایه های داخل اثر
متن يادداشت
Includes bibliographical references.
یادداشتهای مربوط به مندرجات
متن يادداشت
Intro; Preface; Contents; About the Editors; The Stochastic Finite Volume Method; 1 Introduction; 1.1 Deterministic Scalar Hyperbolic Conservation Laws; 1.2 Stochastic Conservation Laws; 1.3 Random Fields and Probability Spaces; 2 General Framework; 2.1 General Principles; 2.2 A First Example: The Kraichnan-Orszag Three-Mode Problem; 2.2.1 One Random Variable; 2.2.2 Two Random Variables; 3 Stochastic Finite Volume Method on Cartesian Grids; 3.1 Stochastic Finite Volume Method; 3.2 Numerical Convergence Analysis; 3.3 Numerical Results; 3.3.1 Buckley-Leverett Equation
متن يادداشت
3.1 Decomposition of the Transport Solution4 Uncertainty Propagation in Transport Equations; 4.1 Uncertainty Modeling for the Constitutive Coefficients; 4.1.1 Stationarity, Ergodicity, and Mixing Properties; 4.2 Homogenization Result and the Convergence Rate; 4.3 Central Limit Theory for the Random Fluctuations; 4.4 Further Remarks; 4.4.1 Long Range Correlated Random Media; 4.4.2 Moments Estimates for Mixing Random Fields; References; Numerical Methods for High-Dimensional Kinetic Equations; 1 Introduction; 2 Numerical Methods; 2.1 Sparse Grids; 2.2 Low-Rank Tensor Approximation
متن يادداشت
3.10 Anisotropic Mesh Adaptation for Euler Equations3.11 Numerical Approximation of the Probability Density Function; 4 Stochastic Finite Volume Method on Unstructured Grids; 4.1 Mixed DG/FV Formulation; 4.2 Numerical Results; 4.2.1 Stochastic Cloud-Shock Interaction Problem (Random Flux); 4.2.2 Forward-Facing Step Channel; 4.2.3 Stochastic Cloud-Shock Interaction Problem (Random IC); 4.2.4 Flow Past a Cylinder; 4.2.5 Flow Around NACA0012 Airfoil; 4.2.6 Flow Around NACA23012 Airfoil with Flap; 4.2.7 Flow Around RAE2822 Airfoil; 4.3 Parallel Algorithm and Parallel Efficiency of the SFVM
متن يادداشت
3.3.2 Stochastic Sod's Shock Tube Problem with Random Initial Data3.3.3 Stochastic Sod's Shock Tube Problem with Random Flux and Initial Data; 3.4 Adaptive Parametrization of the Stochastic Space for SFVM; 3.5 Efficiency of the SFVM; 3.6 SFVM Error Estimates for the Statistical Solution; 3.7 Estimates in L∞-Norm; 3.7.1 Error Estimate for the Mean Eh[uh]; 3.7.2 Error Estimate for the Variance Vh[uh]; 3.8 Estimates in L1-Norm; 3.8.1 Convergence of Eh[uhxy] in L1-Norm; 3.8.2 Convergence of Vh[uhxy] in L1-Norm; 3.9 Error vs Work Estimates for SFVM
متن يادداشت
5 Other Applications5.1 Nozzle Flow with Shock; 5.2 Application with Other Schemes; 5.3 Overcoming the Curse of Dimensionality; 5.4 Applications for Multiphase Flows; 6 Conclusions; References; Uncertainty Modeling and Propagation in Linear Kinetic Equations; 1 Introduction; 2 Uncertainties in the Derivation of Kinetic Equations; 2.1 Setting of the Problem; 2.2 The Paraxial Regime; 2.3 High Frequency Limit; 2.3.1 The Wave Equation; 2.3.2 The Schrödinger Equation; 2.4 Corrector Analysis; 2.4.1 The Itô-Schrödinger Regime; 2.4.2 Other Regimes; 3 Transport Equation
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عنوان
Uncertainty quantification for hyperbolic and kinetic equations.