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Mikhail Pavlovich Galanin - One of the best experts on this subject based on the ideXlab platform.
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nonlinear monotonization of the babenko scheme for the quasi linear Advection Equation 1
Mathematical Modelling and Analysis, 2005Co-Authors: T A Alexandrikova, Mikhail Pavlovich GalaninAbstract:Abstract The paper is devoted to construction and development of new method for numerical solution of hyperbolic type Equations [14, 17]. In the previous papers [4, 5, 6, 7, 8, 9] authors have investigated theoretically and tested experimentally 26 different finite‐difference schemes on 4 point patterns for the simplest hyperbolic Equation: linear Advection Equation. This Equation has the main features of every hyperbolic Equation and is the important part of many mathematical models. In other cases the Advection operator is the important part of the full operator of the problem. All 26 schemes have been compared experimentally on the special representative set of tests. Nevertheless to simplicity of the Equation, almost all schemes have different disadvantages. They are discussed in detail in the cited papers. So, the investigation of new schemes for this Equation is still an important task. In [4, 5, 6, 7, 8, 9] some new schemes were constructed for solving this Advection Equation. The nonlinear monoton...
Margarita Miranda Hernandez - One of the best experts on this subject based on the ideXlab platform.
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space time fractional diffusion Advection Equation with caputo derivative
Abstract and Applied Analysis, 2014Co-Authors: Jose Francisco Gomez Aguilar, Margarita Miranda HernandezAbstract:An alternative construction for the space-time fractional diffusion-Advection Equation for the sedimentation phenomena is presented. The order of the derivative is considered as , for the space and time domain, respectively. The fractional derivative of Caputo type is considered. In the spatial case we obtain the fractional solution for the underdamped, undamped, and overdamped case. In the temporal case we show that the concentration has amplitude which exhibits an algebraic decay at asymptotically large times and also shows numerical simulations where both derivatives are taken in simultaneous form. In order that the Equation preserves the physical units of the system two auxiliary parameters and are introduced characterizing the existence of fractional space and time components, respectively. A physical relation between these parameters is reported and the solutions in space-time are given in terms of the Mittag-Leffler function depending on the parameters and . The generalization of the fractional diffusion-Advection Equation in space-time exhibits anomalous behavior.
Yousra Gati - One of the best experts on this subject based on the ideXlab platform.
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mathematical analysis of a nonlinear parabolic Equation arising in the modelling of non newtonian flows
Siam Journal on Mathematical Analysis, 2005Co-Authors: Eric Cances, Isabelle Catto, Yousra GatiAbstract:The mathematical properties of a nonlinear parabolic Equation arising in the modelling of concentrated suspension flows are investigated. The peculiarity of this Equation is that it may degenerate into a hyperbolic Equation (in fact, a linear Advection Equation). Depending on the initial data, at least two situations can be encountered: the Equation may have a unique solution in a convenient class, or it may have infinitely many solutions. The present article is the theoretical side of a joint project with rheologists, aiming at better understanding the flows of complex fluids.
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mathematical analysis of a nonlinear parabolic Equation arising in the modelling of non newtonian flows
arXiv: Analysis of PDEs, 2003Co-Authors: Eric Cances, Isabelle Catto, Yousra GatiAbstract:The mathematical properties of a nonlinear parabolic Equation arising in the modelling of non-newtonian flows are investigated. The peculiarity of this Equation is that it may degenerate into a hyperbolic Equation (in fact a linear Advection Equation). Depending on the initial data, at least two situations can be encountered: the Equation may have a unique solution in a convenient class, or it may have infinitely many solutions.
George Em Karniadakis - One of the best experts on this subject based on the ideXlab platform.
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long term behavior of polynomial chaos in stochastic flow simulations
Computer Methods in Applied Mechanics and Engineering, 2006Co-Authors: Xiaoliang Wan, George Em KarniadakisAbstract:In this paper we focus on the long-term behavior of generalized polynomial chaos (gPC) and multi-element generalized polynomial chaos (ME-gPC) for partial differential Equations with stochastic coefficients. First, we consider the one-dimensional Advection Equation with a uniform random transport velocity and derive error estimates for gPC and ME-gPC discretizations. Subsequently, we extend these results to other random distributions and high-dimensional random inputs with numerical verification using the algebraic convergence rate of ME-gPC. Finally, we apply our results to noisy flow past a stationary circular cylinder. Simulation results demonstrate that ME-gPC is effective in improving the accuracy of gPC for a long-term integration whereas high-order gPC cannot capture the correct asymptotic behavior.
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spectral polynomial chaos solutions of the stochastic Advection Equation
Journal of Scientific Computing, 2002Co-Authors: M Jardak, George Em KarniadakisAbstract:We present a new algorithm based on Wiener–Hermite functionals combined with Fourier collocation to solve the Advection Equation with stochastic transport velocity. We develop different stategies of representing the stochastic input, and demonstrate that this approach is orders of magnitude more efficient than Monte Carlo simulations for comparable accuracy.
Kozel Karel - One of the best experts on this subject based on the ideXlab platform.
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MODIFIED Equation FOR A CLASS OF EXPLICIT AND IMPLICIT SCHEMES SOLVING ONE-DIMENSIONAL Advection PROBLEM
'Czech Technical University in Prague - Central Library', 2021Co-Authors: Bodnár Tomáš, Fraunié Philippe, Kozel KarelAbstract:This paper presents the general modified Equation for a family of finite-difference schemes solving one-dimensional Advection Equation. The whole family of explicit and implicit schemes working at two time-levels and having three point spatial support is considered. Some of the classical schemes (upwind, Lax-Friedrichs, Lax-Wendroff) are discussed as examples, showing the possible implications arising from the modified Equation to the properties of the considered numerical methods
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MODIFIED Equation FOR A CLASS OF EXPLICIT AND IMPLICIT SCHEMES SOLVING ONE-DIMENSIONAL Advection PROBLEM
'Czech Technical University in Prague - Central Library', 2021Co-Authors: Bodnár Tomáš, Fraunié Philippe, Kozel KarelAbstract:International audienceThis paper presents the general modified Equation for a family of finite-difference schemes solving one-dimensional Advection Equation. The whole family of explicit and implicit schemes working at two time-levels and having three point spatial support is considered. Some of the classical schemes (upwind, Lax-Friedrichs, Lax-Wendroff) are discussed as examples, showing the possible implications arising from the modified Equation to the properties of the considered numerical methods