In this paper,we carry out an analysis of the structural properties of the solutions to the speed gradient(SG)traffic flow model.Under the condition that the relaxation effect can be neglected,it is shown that a 1-sho...In this paper,we carry out an analysis of the structural properties of the solutions to the speed gradient(SG)traffic flow model.Under the condition that the relaxation effect can be neglected,it is shown that a 1-shock or a 1-rarefaction is associated with the first characteristic,but on the other hand,a contact discontinuity rather than a 2-shock or a 2-rarefaction is associated with the second characteristic.Since the existence of a 2-shock or 2-rarefaction violates the physical mechanism of the traffic flow,the SG model is more reasonable.If the relaxation effect cannot be neglected,it is somewhat difficult to carry out the analytical analysis and the numerical simulation results should be obtained.展开更多
We study the relaxation limit for the Aw-Rascle system of traffic flow. For this we apply the theory of invariant regions and the compensated compactness method to get global existence of Cauchy problem for a particul...We study the relaxation limit for the Aw-Rascle system of traffic flow. For this we apply the theory of invariant regions and the compensated compactness method to get global existence of Cauchy problem for a particular Aw-Rascle system with source, where the source is the relaxation term, and we show the convergence of this solutions to the equilibrium state.展开更多
In this article we present a new family of high order accurate Arbitrary Lagrangian-Eulerian one-step WENO finite volume schemes for the solution of stiff hyperbolic balance laws.High order accuracy in space is obtain...In this article we present a new family of high order accurate Arbitrary Lagrangian-Eulerian one-step WENO finite volume schemes for the solution of stiff hyperbolic balance laws.High order accuracy in space is obtained with a standard WENO reconstruction algorithm and high order in time is obtained using the local space-time discontinuous Galerkinmethod recently proposed in[20].In the Lagrangian framework considered here,the local space-time DG predictor is based on a weak formulation of the governing PDE on a moving space-time element.For the spacetime basis and test functions we use Lagrange interpolation polynomials defined by tensor-product Gauss-Legendre quadrature points.The moving space-time elements are mapped to a reference element using an isoparametric approach,i.e.the spacetime mapping is defined by the same basis functions as the weak solution of the PDE.We show some computational examples in one space-dimension for non-stiff and for stiff balance laws,in particular for the Euler equations of compressible gas dynamics,for the resistive relativistic MHD equations,and for the relativistic radiation hydrodynamics equations.Numerical convergence results are presented for the stiff case up to sixth order of accuracy in space and time and for the non-stiff case up to eighth order of accuracy in space and time.展开更多
基金The project supported by the National Natural Science Foundation of China(10272101)
文摘In this paper,we carry out an analysis of the structural properties of the solutions to the speed gradient(SG)traffic flow model.Under the condition that the relaxation effect can be neglected,it is shown that a 1-shock or a 1-rarefaction is associated with the first characteristic,but on the other hand,a contact discontinuity rather than a 2-shock or a 2-rarefaction is associated with the second characteristic.Since the existence of a 2-shock or 2-rarefaction violates the physical mechanism of the traffic flow,the SG model is more reasonable.If the relaxation effect cannot be neglected,it is somewhat difficult to carry out the analytical analysis and the numerical simulation results should be obtained.
文摘We study the relaxation limit for the Aw-Rascle system of traffic flow. For this we apply the theory of invariant regions and the compensated compactness method to get global existence of Cauchy problem for a particular Aw-Rascle system with source, where the source is the relaxation term, and we show the convergence of this solutions to the equilibrium state.
基金the European Research Council under the European Union’s Seventh Framework Programme(FP7/2007-2013)under the research project STiMulUs,ERC Grant agreement no.278267.
文摘In this article we present a new family of high order accurate Arbitrary Lagrangian-Eulerian one-step WENO finite volume schemes for the solution of stiff hyperbolic balance laws.High order accuracy in space is obtained with a standard WENO reconstruction algorithm and high order in time is obtained using the local space-time discontinuous Galerkinmethod recently proposed in[20].In the Lagrangian framework considered here,the local space-time DG predictor is based on a weak formulation of the governing PDE on a moving space-time element.For the spacetime basis and test functions we use Lagrange interpolation polynomials defined by tensor-product Gauss-Legendre quadrature points.The moving space-time elements are mapped to a reference element using an isoparametric approach,i.e.the spacetime mapping is defined by the same basis functions as the weak solution of the PDE.We show some computational examples in one space-dimension for non-stiff and for stiff balance laws,in particular for the Euler equations of compressible gas dynamics,for the resistive relativistic MHD equations,and for the relativistic radiation hydrodynamics equations.Numerical convergence results are presented for the stiff case up to sixth order of accuracy in space and time and for the non-stiff case up to eighth order of accuracy in space and time.
