共查询到20条相似文献，搜索用时 15 毫秒
1.
1.IntroductionIn[1],JinandXinconstructedaclassofthelocalrelaxationapproximation--TheRelaxingSchemesforsystemsofnonlinearcollservationlawsorsinglenonlinearconservationlawson,dofi(u)~ ;ac~0,(1l)otMoxil=1zwithinitialdatau(0,x)~\"o(x),x~(xl,...,-cd),byusingtheideaofthelocalrelaxationapproximation[1--4].Theschemeisobtainedinthefollowingway:firstalinearhyperbolicsystemwithastiffsourcetermisconstructedtoapproximatetheoriginalsystem(1.1)withasmalldissipativecorrection;Then,thenewlinearhyperbolicsyste… 相似文献
2.
Hua-zhong Tang Hua-mu Wu 《计算数学(英文版)》2001,(3)
1. IntroductionWe are illterested in the numerical approximation of viscosity solution of the following lirstorder Hamilton-Jacobi eqllationopt + H(&.,, rk..' ...) gb'.) - 0' (1'1)with initial data ac(~, 0) = ado(x). It is well known that the solutions to problem (1.1) typicallyare continuous (typically they are locally Lipschitz continuous) but with discoatinuous derivatives, even though the initial data ado E Coo. The nonuniqueness of such solutions to (1.1) alsonecessitates the introducti… 相似文献
3.
１．引言本文研究如下非线性刚性守恒律方程组的全隐式差分逼近． 方程（1．１）中的源项ｇ（ｕ,ｖ）定义为 ｇ（ｕ,ｖ）＝ｖ－（１－μ）ｆ（ｕ）,（１．２）其中ｆ是ｕ的一个给定函数,δ是一个小正参数,称为松弛时间,μ是参数．方程组（１．１）频繁出现于粘弹性力学中． 在零松弛时间限（δ→０）下,从（１．１）可得到如下方程组该方程组通常称为“平衡”模型,而方程组（１．１）称为“非平衡”模型． 文中将假设μ满足 ０＜ μ＜ １,（１．４）以便保证拟稳定性条件［１９,２０］和次特征条件［１１,２,３］： λ１≤λ＊… 相似文献
4.
Hua-zhong Tang 《计算数学(英文版)》2001,19(6):571-582
1. IntroductionWe are interested in construction of the central reltalng sChemes for system of noIilinearhyperbolic conservation lawswith initial data U(0, x) = Uo(x), x = (x1 ? ...! xd), based on the local relaJxation approkimationof Eq.(1.1) [2, 3, 6, 8, 9, 12].To i11ustrate the basic idea of the relaalng schemes, for the sake of simplicity in the presentation, we restrict our attention to onedimensional scalar conservaioll lawsFirst, introduce a linear hyperbollc system with a stiff sourc… 相似文献
5.
Christophe Berthon. 《Mathematics of Computation》2006,75(256):1809-1831
We propose a numerical scheme to approximate the weak solutions of the 10-moment Gaussian closure. The moment Gaussian closure for gas dynamics is governed by a conservative hyperbolic system supplemented by entropy inequalities whose solutions satisfy positiveness of density and tensorial pressure. We consider a Suliciu-type relaxation numerical scheme to approximate the solutions. These methods are proved to satisfy all the expected positiveness properties and all the discrete entropy inequalities. The scheme is illustrated by several numerical experiments.
6.
New first- and high-order centred methods for conservation lawsare presented. Convenient TVD conditions for constructing centredTVD schemes are then formulated and some useful results areproved. Two families of centred TVD schemes are constructedand extended to nonlinear systems. Some numerical results arealso presented. 相似文献
7.
Gianmarco Manzini 《Numerical Methods for Partial Differential Equations》2009,25(5):1029-1066
We have developed an efficient hybrid technique for solving nonlinear conservation laws. Previous hybrid techniques have been accurate but lacked the property of conservation, whereas our technique is both accurate and conservative. To achieve this, we superimposed all possible stencils for ENO polynomials and weighted the value from each cells in a way that depends on the numerical solution. Computational efficiency relies on switching from central data where the exact solution is smooth to noncentral data near discontinuities. We prove the theoretical consistency of the technique and discuss the connection with ENO and WENO methods. We introduce time dependency by combining our method with Runge‐Kutta schemes that are TVD preserving. We have verified our technique experimentally by solving a suite of test problems with convex and non‐convex flux functions taken from the literature. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2009 相似文献
8.
Tong Yang Huijiang Zhao Changjiang Zhu 《Proceedings of the American Mathematical Society》2003,131(4):1257-1266
We give uniform BV estimates and -stability of Lax-Friedrichs' scheme for a class of systems of strictly hyperbolic conservation laws whose integral curves of the eigenvector fields are straight lines, i.e., Temple class, under the assumption of small total variation. This implies that the approximate solutions generated via the Lax-Friedrichs' scheme converge to the solution given by the method of vanishing viscosity or the Godunov scheme, and then the Glimm scheme or the wave front tracking method.
9.
Following Ben-Artzi and LeFloch, we consider nonlinear hyperbolic conservation laws posed on a Riemannian manifold, and we establish an L1-error estimate for a class of finite volume schemes allowing for the approximation of entropy solutions to the initial value problem. The error in the L1 norm is of order h1/4 at most, where h represents the maximal diameter of elements in the family of geodesic triangulations. The proof relies on a suitable generalization of Cockburn, Coquel, and LeFloch＇s theory which was originally developed in the Euclidian setting. We extend the arguments to curved manifolds, by taking into account the effects to the geometry and overcoming several new technical difficulties. 相似文献
10.
Huazhong Tang;Gerald Warnecke 《Mathematical Modelling and Numerical Analysis》2004,38(2):345-357
First–order accurate monotone conservative schemes have goodconvergence and stability properties, and thus play a veryimportant role in designing modern high resolution shock-capturingschemes.Do the monotone difference approximations alwaysgive a good numerical solution in sense of monotonicity preservationor suppression of oscillations? This note will investigate this problemfrom a numerical point of view and show thata (2K+1) -point monotone scheme may give an oscillatory solutioneven though the approximate solution is total variation diminishing, andsatisfies maximum principle as well as discrete entropy inequality.https://doi.org/10.1051/m2an:2004016 相似文献
11.
Xiaohan Cheng Yufeng Nie Jianhu Feng Li Cai 《Journal of Applied Analysis & Computation》2015,5(3):453-464
A high order central-upwind scheme for approximating hyperbolic conservation laws is proposed. This construction is based on the evaluation of the local propagation speeds of the discontinuities and Peer's fourth order non-oscillatory reconstruction. The presented scheme shares the simplicity of central schemes, namely no Riemann solvers are involved. Furthermore, it avoids alternating between two staggered grids, which is particularly a challenge for problems which involve complex geometries and boundary conditions. Numerical experiments demonstrate the high resolution and non-oscillatory properties of our scheme. 相似文献
12.
Ritesh Kumar Dubey 《Applied mathematics and computation》2010,215(9):3335-3342
In this work a first order accurate semi-conservative composite scheme is presented for hyperbolic conservation laws. The idea is to consider the non-conservative form of conservation law and utilize the explicit wave propagation direction to construct semi-conservative upwind scheme. This method captures the shock waves exactly with less numerical dissipation but generates unphysical rarefaction shocks in case of expansion waves with sonic points. It shows less dissipative nature of constructed scheme. In order to overcome it, we use the strategy of composite schemes. A very simple criteria based on wave speed direction is given to decide the iterations. The proposed method is applied to a variety of test problems and numerical results show accurate shock capturing and higher resolution for rarefaction fan. 相似文献
13.
14.
In this paper, we developed a class of the fourth order accurate finite volume Hermite weighted essentially non-oscillatory (HWENO) schemes based on the work (Computers & Fluids, 34: 642–663 (2005)) by Qiu and Shu, with Total Variation Diminishing Runge-Kutta time discretization method for the two-dimensional hyperbolic conservation laws. The key idea of HWENO is to evolve both with the solution and its derivative, which allows for using Hermite interpolation in the reconstruction phase, resulting in a more compact stencil at the expense of the additional work. The main difference between this work and the formal one is the procedure to reconstruct the derivative terms. Comparing with the original HWENO schemes of Qiu and Shu, one major advantage of new HWENO schemes is its robust in computation of problem with strong shocks. Extensive numerical experiments are performed to illustrate the capability of the method. Corresponding author This work was partially supported by the National Natural Science Foundation of China (Grant No. 10671097), the European project ADIGMA on the development of innovative solution algorithms for aerodynamic simulations, Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry and the Natural Science Foundation of Jiangsu Province (Grant No. BK2006511) 相似文献
15.
Hua-zhong Tang 《计算数学(英文版)》2001,19(5):511-518
1. IntroductionThis paPer is interested in studies of the cell eatroPy ineqallty for two classes of the fullydiscrete relaxin schemes aPprchating the fOlfowing scalar consendion lawwith dritial data u(0, x) = bo(x), x = (x1, ...) xd).lt is wen knOWn that the above cauchy problem (1.1) may not ahas have a smooth globalsollltion even thOugh the initial data uo is smoOth [8, 9]. Thus, we consider its weak solutiOn sothat the prObem (1.1) ndght hav a global solution allOwing disconinulies (e.g… 相似文献
16.
For hyperbolic systems of balance laws with source manifesting relaxation, it is shown that the Kawashima condition, which yields global classical solutions with smooth initial values near equilibrium, is also instrumental in inducing the existence of global admissible BV solutions, accommodating shocks. 相似文献
17.
Stefano Bianchini Rinaldo M. Colombo 《Proceedings of the American Mathematical Society》2002,130(7):1961-1973
We consider the dependence of the entropic solution of a hyperbolic system of conservation laws
on the flux function . We prove that the solution is Lipschitz continuous w.r.t. the norm of the derivative of the perturbation of . We apply this result to prove the convergence of the solution of the relativistic Euler equation to the classical limit.
on the flux function . We prove that the solution is Lipschitz continuous w.r.t. the norm of the derivative of the perturbation of . We apply this result to prove the convergence of the solution of the relativistic Euler equation to the classical limit.
18.
Monotone absolutely stable conservative difference schemes intended for solving quasilinear multidimensional hyperbolic equations are described. For sufficiently smooth solutions, the schemes are fourth-order accurate in each spatial direction and can be used in a wide range of local Courant numbers. The order of accuracy in time varies from the third for the smooth parts of the solution to the first near discontinuities. This is achieved by choosing special weighting coefficients that depend locally on the solution. The presented schemes are numerically efficient thanks to the simple two-diagonal (or block two-diagonal) structure of the matrix to be inverted. First the schemes are applied to system of nonlinear multidimensional conservation laws. The choice of optimal weighting coefficients for the schemes of variable order of accuracy in time and flux splitting is discussed in detail. The capabilities of the schemes are demonstrated by computing well-known two-dimensional Riemann problems for gasdynamic equations with a complex shock wave structure. 相似文献
19.
Huazhong Tang & Yuhuan Yuan 《计算数学(英文版)》2020,38(5):768-796
This paper studies the two-stage fourth-order accurate time discretization [J.Q. Li andZ.F. Du, SIAM J. Sci. Comput., 38 (2016)] and its application to the special relativistic hydrodynamical equations. Our analysis reveals that the new two-stage fourth-orderaccurate time discretizations can be proposed. With the aid of the direct Eulerian GRP(generalized Riemann problem) methods and the analytical resolution of the local \"quasi1D\" GRP, the two-stage fourth-order accurate time discretizations are successfully implemented for the 1D and 2D special relativistic hydrodynamical equations. Several numerical experiments demonstrate the performance and accuracy as well as robustness of ourschemes. 相似文献
20.
A. Chalabi. 《Mathematics of Computation》1999,68(227):955-970
We focus in this study on the convergence of a class of relaxation numerical schemes for hyperbolic scalar conservation laws including stiff source terms. Following Jin and Xin, we use as approximation of the scalar conservation law, a semi-linear hyperbolic system with a second stiff source term. This allows us to avoid the use of a Riemann solver in the construction of the numerical schemes. The convergence of the approximate solution toward a weak solution is established in the cases of first and second order accurate MUSCL relaxed methods.