The Experts below are selected from a list of 17217 Experts worldwide ranked by ideXlab platform
Shuyang Xiang - One of the best experts on this subject based on the ideXlab platform.
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Existence theory for well-balanced Euler model.
arXiv: Analysis of PDEs, 2019Co-Authors: Shuyang Xiang, Yangyang CaoAbstract:We study the initial value problem for a kind of Euler equation with a source term. Our main result is the existence of a globally-in-time weak solution whose total variation is bounded on the the domain of definition, allowing the existence of shock waves. Our proof relies on a well-balanced Random Choice Method called Glimm Method which preserves the fluid equilibria and we construct a sequence of approximate weak solutions which converges to the exact weak solution of the initial value problem, based on the construction of exact solutions of the generalized Riemann problem associated with initially piecewise steady state solutions.
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weakly regular fluid flows with bounded variation on the domain of outer communication of a schwarzschild black hole spacetime
Journal de Mathématiques Pures et Appliquées, 2016Co-Authors: Philippe G Lefloch, Shuyang XiangAbstract:Abstract We study the global dynamics of isothermal fluids evolving in the domain of outer communication of a Schwarzschild black hole. We first formulate the initial value problem within a class of weak solutions with bounded variation (BV), possibly containing shock waves. We then introduce a version of the Random Choice Method and establish a global-in-time existence theory for the initial value problem within the proposed class of weakly regular fluid flows. The initial data may have arbitrary large bounded variation and can possibly blow up near the horizon of the black hole. Furthermore, we study the class of possibly discontinuous, equilibrium solutions and design a version of the Random Choice Method in which these fluid equilibria are exactly preserved. This leads us to a nonlinear stability property for fluid equilibria under small perturbations with bounded variation. Furthermore, we can also encompass several limiting regimes (stiff matter, non-relativistic flows, extremal black hole) by letting the physical parameters (mass of the black hole, light speed, sound speed) reach extremal values.
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Weakly regular fluid flows with bounded variation on a Schwarzschild background
arXiv: Analysis of PDEs, 2015Co-Authors: Philippe G Lefloch, Shuyang XiangAbstract:We study the global dynamics of isothermal fluids evolving in the domain of outer communication of a Schwarzschild black hole. We first formulate the initial value problem within a class of weak solutions with bounded variation (BV), possibly containing shock waves. We then introduce a version of the Random Choice Method and establish a global-in-time existence theory for the initial value problem within the proposed class of weakly regular fluid flows. The initial data may have arbitrary large bounded variation and can possibly blow up near the horizon of the black hole. Furthermore, we study the class of possibly discontinuous, equilibrium solutions and design a version of the Random Choice Method in which these fluid equilibria are exactly preserved. This leads us to a nonlinear stability property for fluid equilibria under small perturbations with bounded variation. Furthermore, we can also encompass several limiting regimes (stiff matter, non-relativistic flows, extremal black hole) by letting the physical parameters (mass of the black hole, light speed, sound speed) reach extremal values.
Wai How Hui - One of the best experts on this subject based on the ideXlab platform.
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An investigation of Random Choice Method for three‐dimensional steady supersonic flows
International Journal for Numerical Methods in Fluids, 1999Co-Authors: Ching-yuen Loh, Meng-sing Liou, Wai How HuiAbstract:In this paper, an unsplit Random Choice Method (RCM) is developed and applied to numerically solve three-dimensional supersonic steady flow problems. In order to keep the contacts (slip surfaces) crisply resolved, a new Lagrangian formulation is employed. Due to the lack of exact solutions to 3D Riemann problems, approximate Riemann solutions in the weak sense are adopted. The RCM is thus as efficient as the deterministic TVD schemes, and yields almost identical results in the model problems. Copyright © 1999 John Wiley & Sons, Ltd.
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lagrangian Random Choice Method for steady two dimensional supersonic hypersonic flow
AIAA Journal, 1993Co-Authors: C. Y. Loh, Wai How HuiAbstract:Glimm's (1965) Random Choice Method has been successfully applied to compute steady two-dimensional supersonic/hypersonic flow using a new Lagrangian formulation. The Method is easy to program, fast to execute, yet it is very accurate and robust. It requires no grid generation, resolves slipline and shock discontinuities crisply, can handle boundary conditions most easily, and is applicable to hypersonic as well as supersonic flow. It represents an accurate and fast alternative to the existing Eulerian Methods. Many computed examples are given.
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Lagrangian Random Choice Method for steady two-dimensional supersonic/hypersonic flow
AIAA Journal, 1993Co-Authors: C. Y. Loh, Wai How HuiAbstract:Glimm's (1965) Random Choice Method has been successfully applied to compute steady two-dimensional supersonic/hypersonic flow using a new Lagrangian formulation. The Method is easy to program, fast to execute, yet it is very accurate and robust. It requires no grid generation, resolves slipline and shock discontinuities crisply, can handle boundary conditions most easily, and is applicable to hypersonic as well as supersonic flow. It represents an accurate and fast alternative to the existing Eulerian Methods. Many computed examples are given.
Zhen Dong - One of the best experts on this subject based on the ideXlab platform.
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ROLLING OF SHIPS UNDER SHIPPING WATER CONDITION
1991Co-Authors: X Huang, Zhen DongAbstract:This paper deals with the problems associated with the effect of water shifting on a ship rolling in beam sea. The motion of deck water is modelled by shallow water equation and solved by Glimm's Random Choice Method. The hydrodynamic forces acting on the ship are determined by boundary element approach in time domain. The motion of the ship and the deck water are calculated and illustrated. Although only two dimensional cases are considered for the sake of simplicity, the calculation can easily be extended to a full scale ship by using the strip Method.
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THE ROLLING MOTION UNDER THE SHIPPING WATER CONDITION
1990Co-Authors: X Huang, Zhen DongAbstract:The paper deals with the problems associated with the effect of shipping water on the rolling of a ship in beam seas. The motion of the deck water is modelled using shallow water equations and solved using Grimm's Random Choice Method. The hydrodynamic forces acting on the ship are determined by a boundary element approach in the time domain. The motions of the ship and deck water are calculated and illustrated graphically. For the sake of simplicity, only a two dimensional case is studied. However, the authors point out that there is no obstacle to extending the calculation to a full scale ship by using the strip Method.
Philippe G Lefloch - One of the best experts on this subject based on the ideXlab platform.
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weakly regular fluid flows with bounded variation on the domain of outer communication of a schwarzschild black hole spacetime
Journal de Mathématiques Pures et Appliquées, 2016Co-Authors: Philippe G Lefloch, Shuyang XiangAbstract:Abstract We study the global dynamics of isothermal fluids evolving in the domain of outer communication of a Schwarzschild black hole. We first formulate the initial value problem within a class of weak solutions with bounded variation (BV), possibly containing shock waves. We then introduce a version of the Random Choice Method and establish a global-in-time existence theory for the initial value problem within the proposed class of weakly regular fluid flows. The initial data may have arbitrary large bounded variation and can possibly blow up near the horizon of the black hole. Furthermore, we study the class of possibly discontinuous, equilibrium solutions and design a version of the Random Choice Method in which these fluid equilibria are exactly preserved. This leads us to a nonlinear stability property for fluid equilibria under small perturbations with bounded variation. Furthermore, we can also encompass several limiting regimes (stiff matter, non-relativistic flows, extremal black hole) by letting the physical parameters (mass of the black hole, light speed, sound speed) reach extremal values.
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Weakly regular fluid flows with bounded variation on a Schwarzschild background
arXiv: Analysis of PDEs, 2015Co-Authors: Philippe G Lefloch, Shuyang XiangAbstract:We study the global dynamics of isothermal fluids evolving in the domain of outer communication of a Schwarzschild black hole. We first formulate the initial value problem within a class of weak solutions with bounded variation (BV), possibly containing shock waves. We then introduce a version of the Random Choice Method and establish a global-in-time existence theory for the initial value problem within the proposed class of weakly regular fluid flows. The initial data may have arbitrary large bounded variation and can possibly blow up near the horizon of the black hole. Furthermore, we study the class of possibly discontinuous, equilibrium solutions and design a version of the Random Choice Method in which these fluid equilibria are exactly preserved. This leads us to a nonlinear stability property for fluid equilibria under small perturbations with bounded variation. Furthermore, we can also encompass several limiting regimes (stiff matter, non-relativistic flows, extremal black hole) by letting the physical parameters (mass of the black hole, light speed, sound speed) reach extremal values.
C. Y. Loh - One of the best experts on this subject based on the ideXlab platform.
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lagrangian Random Choice Method for steady two dimensional supersonic hypersonic flow
AIAA Journal, 1993Co-Authors: C. Y. Loh, Wai How HuiAbstract:Glimm's (1965) Random Choice Method has been successfully applied to compute steady two-dimensional supersonic/hypersonic flow using a new Lagrangian formulation. The Method is easy to program, fast to execute, yet it is very accurate and robust. It requires no grid generation, resolves slipline and shock discontinuities crisply, can handle boundary conditions most easily, and is applicable to hypersonic as well as supersonic flow. It represents an accurate and fast alternative to the existing Eulerian Methods. Many computed examples are given.
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Lagrangian Random Choice Method for steady two-dimensional supersonic/hypersonic flow
AIAA Journal, 1993Co-Authors: C. Y. Loh, Wai How HuiAbstract:Glimm's (1965) Random Choice Method has been successfully applied to compute steady two-dimensional supersonic/hypersonic flow using a new Lagrangian formulation. The Method is easy to program, fast to execute, yet it is very accurate and robust. It requires no grid generation, resolves slipline and shock discontinuities crisply, can handle boundary conditions most easily, and is applicable to hypersonic as well as supersonic flow. It represents an accurate and fast alternative to the existing Eulerian Methods. Many computed examples are given.
