A fourth-order relaxation scheme is derived and applied to hyperbolic systems of conservation laws in one and two space dimensions. The scheme is based on a fourthorder central weighted essentially nonoscillatory （CW...A fourth-order relaxation scheme is derived and applied to hyperbolic systems of conservation laws in one and two space dimensions. The scheme is based on a fourthorder central weighted essentially nonoscillatory （CWENO） reconstruction for one-dimensional cases, which is generalized to two-dimensional cases by the dimension-by-dimension approach. The large stability domain Runge-Kutta-type solver ROCK4 is used for time integration. The resulting method requires neither the use of Riemann solvers nor the computation of Jacobians and therefore it enjoys the main advantage of the relaxation schemes. The high accuracy and high-resolution properties of the present method are demonstrated in one- and two-dimensional numerical experiments.展开更多
In this paper we study the problem of the global existence （in time） of weak entropic solutions to a system of three hyperbolic conservation laws, in one space dimension, for large initial data. The system models th...In this paper we study the problem of the global existence （in time） of weak entropic solutions to a system of three hyperbolic conservation laws, in one space dimension, for large initial data. The system models the dynamics of phase transitions in an isothermal fluid; in Lagrangian coordinates, the phase interfaces are represented as stationary contact discontinuities. We focus on the persistence of solutions consisting in three bulk phases separated by two interfaces. Under some stability conditions on the phase configuration and by a suitable front tracking algorithm we show that, if the BV-norm of the initial data is less than an explicit （large） threshold, then the Cauchy problem has global solutions.展开更多
We study central-upwind schemes for systems of hyperbolic conservation laws,recently introduced in[13].Similarly to staggered non-oscillatory central schemes,these schemes are central Godunov-type projection-evolution...We study central-upwind schemes for systems of hyperbolic conservation laws,recently introduced in[13].Similarly to staggered non-oscillatory central schemes,these schemes are central Godunov-type projection-evolution methods that enjoy the advantages of high resolution,simplicity,universality and robustness.At the same time,the central-upwind framework allows one to decrease a relatively large amount of numerical dissipation present at the staggered central schemes.In this paper,we present a modification of the one-dimensional fully-and semi-discrete central-upwind schemes,in which the numerical dissipation is reduced even further.The goal is achieved by a more accurate projection of the evolved quantities onto the original grid.In the semi-discrete case,the reduction of dissipation procedure leads to a new,less dissipative numerical flux.We also extend the new semi-discrete scheme to the twodimensional case via the rigorous,genuinely multidimensional derivation.The new semi-discrete schemes are tested on a number of numerical examples,where one can observe an improved resolution,especially of the contact waves.展开更多
This study presents a modification of the central-upwind Kurganov scheme for approximating the solution of the 2D Euler equation.The prototype,extended from a 1D model,reduces substantially less dissipation than expec...This study presents a modification of the central-upwind Kurganov scheme for approximating the solution of the 2D Euler equation.The prototype,extended from a 1D model,reduces substantially less dissipation than expected.The problem arises from over-restriction of some slope limiters,which keep slopes between interfaces of cells to be Total-Variation-Diminishing.This study reports the defect and presents a re-derived optimal formula.Numerical experiments highlight the significance of this formula,especially in long-time,large-scale simulations.展开更多
基金the National Natural Science Foundation of China (60134010)The English text was polished by Yunming Chen.
文摘A fourth-order relaxation scheme is derived and applied to hyperbolic systems of conservation laws in one and two space dimensions. The scheme is based on a fourthorder central weighted essentially nonoscillatory （CWENO） reconstruction for one-dimensional cases, which is generalized to two-dimensional cases by the dimension-by-dimension approach. The large stability domain Runge-Kutta-type solver ROCK4 is used for time integration. The resulting method requires neither the use of Riemann solvers nor the computation of Jacobians and therefore it enjoys the main advantage of the relaxation schemes. The high accuracy and high-resolution properties of the present method are demonstrated in one- and two-dimensional numerical experiments.
文摘In this paper we study the problem of the global existence （in time） of weak entropic solutions to a system of three hyperbolic conservation laws, in one space dimension, for large initial data. The system models the dynamics of phase transitions in an isothermal fluid; in Lagrangian coordinates, the phase interfaces are represented as stationary contact discontinuities. We focus on the persistence of solutions consisting in three bulk phases separated by two interfaces. Under some stability conditions on the phase configuration and by a suitable front tracking algorithm we show that, if the BV-norm of the initial data is less than an explicit （large） threshold, then the Cauchy problem has global solutions.
基金supported in part by the NSF Grant DMS-0310585The work of C.-T.Lin was supported in part by the NSC grants NSC 94-2115-M-126-003 and 91-2115-M-126-001.
文摘We study central-upwind schemes for systems of hyperbolic conservation laws,recently introduced in[13].Similarly to staggered non-oscillatory central schemes,these schemes are central Godunov-type projection-evolution methods that enjoy the advantages of high resolution,simplicity,universality and robustness.At the same time,the central-upwind framework allows one to decrease a relatively large amount of numerical dissipation present at the staggered central schemes.In this paper,we present a modification of the one-dimensional fully-and semi-discrete central-upwind schemes,in which the numerical dissipation is reduced even further.The goal is achieved by a more accurate projection of the evolved quantities onto the original grid.In the semi-discrete case,the reduction of dissipation procedure leads to a new,less dissipative numerical flux.We also extend the new semi-discrete scheme to the twodimensional case via the rigorous,genuinely multidimensional derivation.The new semi-discrete schemes are tested on a number of numerical examples,where one can observe an improved resolution,especially of the contact waves.
文摘This study presents a modification of the central-upwind Kurganov scheme for approximating the solution of the 2D Euler equation.The prototype,extended from a 1D model,reduces substantially less dissipation than expected.The problem arises from over-restriction of some slope limiters,which keep slopes between interfaces of cells to be Total-Variation-Diminishing.This study reports the defect and presents a re-derived optimal formula.Numerical experiments highlight the significance of this formula,especially in long-time,large-scale simulations.
