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.
本文讨论双曲型守恒律方程的熵稳定格式.对于给定的熵对,格式所满足的熵条件中的数值熵通量是不唯一的.Tadmor的充分条件可以唯一地确定标量方程的熵守恒通量,但不能唯一确定方程组的熵守恒通量,却可以给出方程组的空间一阶精度的熵守恒格式.也讨论了在熵守恒通量上添加数值粘性得到的显式熵稳定格式需要满足的条件及常见的时间离散对熵守恒和熵稳定的影响. 相似文献
3.
Hua-zhong Tang 《计算数学(英文版)》2002,(2)
1. IntroductionWe are are interested in the fOllowing Cauchy problem for scalar conservation lawswhere the initial data uo E BV(R) and the flux function f 6 C'(n).It is well known that this problem may not always have a smooth global solution even ifthe i… 相似文献
4.
1.IntroductionAsthesimplestrepresentationofgeneralconservationlaws,thesingleconservationlawswithonespacevariablehavebeenthoroughlydiscussed.Inthecasesthatthefluxfunctionisconvexorconcave,P.D.LaxobtainedageneralexpressionofthesolutionsforCauchyproblems[2];inordertoguaranteetheuniquenessofthesolution,O.A.OlejnikpresentedherfamousE--conditionwhichcanbeappliedtogeneralconservationlawswithonespacevariablel4];TheLax'sconceptsofentropyfunctionsandrelatedinequalityalsocanbeusedinthisspecialcase[3]… 相似文献
5.
Hua-zhong Tang 《计算数学(英文版)》2001,(5)
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
6.
Hua-zhong Tang Gerald Warnecke 《计算数学(英文版)》2006,24(2):121-140
This paper presents a class of high resolution local time step schemes for nonlinear hyperbolic conservation laws and the closely related convection-diffusion equations, by projecting the solution increments of the underlying partial differential equations (PDE) at each local time step. The main advantages are that they are of good consistency, and it is convenient to implement them. The schemes are L^∞ stable, satisfy a cell entropy inequality, and may be extended to the initial boundary value problem of general unsteady PDEs with higher-order spatial derivatives. The high resolution schemes are given by combining the reconstruction technique with a second order TVD Runge-Kutta scheme or a Lax-Wendroff type method, respectively.
The schemes are used to solve a linear convection-diffusion equation, the nonlinear inviscid Burgers' equation, the one- and two-dimensional compressible Euler equations, and the two-dimensional incompressible Navier-Stokes equations. The numerical results show that the schemes are of higher-order accuracy, and efficient in saving computational cost, especially, for the case of combining the present schemes with the adaptive mesh method [15]. The correct locations of the slow moving or stronger discontinuities are also obtained, although the schemes are slightly nonconservative. 相似文献
7.
非凸单个守恒律初边值问题的整体弱熵解的构造 总被引:4,自引:0,他引:4
本文研究具有两段常数的初始值和常数边界值的非凸单个守恒律的初边值问题.在流函数具有一个拐点的条件下,由相应的初始值问题弱熵解的结构和Bardos-Leroux-Nedelec提出的边界熵条件,给出初边值问题整体弱熵解的一个构造方法,澄清弱熵解在边界附近的结构.与严格凸的单个守恒律初边值问题相比,非凸单个守恒律初边值问题的弱熵解中包括下列新的相互作用类型:一个接触或非接触激波碰到边界,边界弹回一个非接触激波. 相似文献
8.
Hua-zhong Tang 《计算数学(英文版)》1999,(4)
1.IntroductionLetusconsidertheCauchyproblemsfornonlinearhyperbolicscalarconservationlaws:wheref:W~WisLipschitzcontinuousfunctions,andtheinitialdata"o(x)isagivenfunctioninLI(R)nLoo(R).Asitiswell--known,thisproblemingeneraldoesnotadmitsmoothsolution,so... 相似文献
9.
一类时空二阶精度高分辨率MmB差分格式的构造及数值试验 总被引:6,自引:0,他引:6
1.引言考虑如下二维双曲型守恒律初值问题的数值解.H.M.Wu和S.L.Yang在文山中给出了MmB差分格式的定义如下:给定(.1)M差分格式定义.若则称格式(1.2)为MmB差分格式.这里BmB表示局部MaximumandminimumBounds.由定义可知,若差分格式(1.2)可写为形式且。\P’三0,>。:r’一1.则格式(1.4)为MmB差分格式.j=l文山构造了二维双曲型守恒律的二类二阶精度的MmB差分格式,使构造二维高分辨格式有了新的突破,但他们是从标量线性双曲型守恒律出发,然后把结果推广到非线性情形.本文直接从二维非线性双曲型守恒律… 相似文献
10.
11.
王靖华 《数学物理学报(B辑英文版)》2009,29(3):613-628
We prove that for a given strictly increasing initial datum in Ck, the solution of the initial value problem is piecewise Ck smooth except for flux functions of nonconvex conservation laws in a certain subset of C^k+1 of first category, defined in the range of the initial datum. 相似文献
12.
一个求解双曲型守恒律方程的高分辨率GVC格式 总被引:1,自引:0,他引:1
朱庆勇 《高等学校计算数学学报》2000,22(2):169-174
1 引 言本文研究双曲型方程:ut+fx=0, t>0,-∞相似文献
13.
刘海亮 《高校应用数学学报(A辑)》1996,(3):277-282
本文研究了非凸双曲守恒律ut+(u^3)x=0解的渐近性态。对于初值具有紧支集或周期函数的情形,我们利用广义特征原理,建立了关于波速总变差的基本递推估计,给出了解的最优衰减速率。 相似文献
14.
This article is concerned with the pointwise error estimates for vanishing vis- cosity approximations to scalar convex conservation laws with boundary.By the weighted error function and a bootstrap extrapolation technique introduced by Tadmor-Tang,an optimal pointwise convergence rate is derived for the vanishing viscosity approximations to the initial-boundary value problem for scalar convex conservation laws,whose weak entropy solution is piecewise C 2 -smooth with interaction of elementary waves and the ... 相似文献
15.
Ning Zhao 《计算数学(英文版)》1998,16(2):179-192
1.IntroductionConsidernumericalsolutionsoftheinitialvalueproblemforhyperbolicconservationlawsinonedimensionwhereu~(.ul,u2,...,"m)"andf(u)~(fi(u),fZ(u),',fm(u))".Andconservationlawsintwodimensionswhereu~(ul,u25...,"m)',f(u)~(fi(u),fZ(u),'?fm(u))',andg(u)~(gi(u),gZ(M),',gm(U))".FOrthescalarconservationlawsinonedimension,theTVDconceptbyA.Ha.te.[3]iswidelyacceptedtodesignthenumericalschemesfortheoreticalpurposesandpracticalapplications.Thetotalvariationofagridfunction{uj}denotedbyTV(u)… 相似文献
16.
Hua-zhong Tang 《计算数学(英文版)》2000,18(3):313-324
1. IntroductionIn [6], Jin and adn constructed a class of uPWind relaxing schemes for nonlinearconservation lawswith initial data u(0, x) ~ "o(x), x ~ (xl, ...t -cd), by using the idea of the local relaxation approximation [2,3,6,10].The relaxing scheme is obtained in the following way: A linear hyperbolic systemwith a stiff source term is first constructed to approximate the original equation (1.1)with a small dissipative correction. Then this linear hyperbolic system is solved easilyby und… 相似文献
17.
封建湖 《纯粹数学与应用数学》1996,12(2):12-16
研究了如何利用迎风格式的耗散性构造中心差分TVD格式的方法,给 相应的定理,构造出新的耗散表达式。新格式既保留了二阶中心差分格式灵活方便的优点,又吸收了迎风格式耗散项比较精细的特点,同时具有TVD性质,使得新格式具有较同的激波分辨率。 相似文献
18.
Mohammed Seaid 《计算数学(英文版)》2007,25(4):440-457
We construct and implement a non-oscillatory relaxation scheme for multidimensional hyperbolic systems of conservation laws. The method transforms the nonlinear hyperbolic system to a semilinear model with a relaxation source term and linear characteristics which can be solved numerically without using either Riemann solver or linear iterations. To discretize the relaxation system we consider a high-resolution reconstruction in space and a TVD Runge-Kutta time integration. Detailed formulation of the scheme is given for problems in three space dimensions and numerical experiments are implemented in both scalar and system cases to show the effectiveness of the method. 相似文献
19.
CONSERVATION OF THREE—POINT COMPACT SCHEMES ON SINGLE AND MULTIBLOCK PATCHED GRIDS FOR HYPERBOLIC PROBLEMS 总被引:1,自引:0,他引:1
Zi-niuWu 《计算数学(英文版)》2003,21(3):383-400
For nonlinear hyperbloic problems,Conservation of the numerical scheme is important for convergence to the correct weak solutions.In this paper the the conservation of the well-known compact scheme up to fourth order of accuracy on a single and uniform grid is studied,and a conservative interface treatment is derived for compact schemes on patched grids .For a pure initial value problem,the compact scheme is shown to be equivalent to a scheme in the usual conservative form .For the case of a mixed initial boundary value problem,the compact scheme is conservative only if the rounding errors are small enough.For a pactched grid interface,a conservative interface condition useful for mesh fefiement and for parallel computation is derived and its order of local accuracy is analyzed. 相似文献
20.
CONVERGENCE OF THE LAX-FRIEDRICHS SCHEME AND STABILITY FOR CONSERVATION LAWS WITH A DISCONTINUOUS SPACE-TIME DEPENDENT FLUX 总被引:4,自引:0,他引:4 下载免费PDF全文
The authors give the first convergence proof for the Lax-Friedrichs finite differencescheme for non-convex genuinely nonlinear scalar conservation laws of the formu_t f(k(x, t), u)_x = 0,where the coefficient k(x, t) is allowed to be discontinuous along curves in the (x, t)plane. In contrast to most of the existing literature on problems with discontinuouscoefficients, here the convergence proof is not based on the singular mapping approach,but rather on the div-curl lemma (but not the Young measure) and a Lax type en-tropy estimate that is robust with respect to the regularity of k(x, t). Following [14],the authors propose a definition of entropy solution that extends the classical Kruzkovdefinition to the situation where k(x, t) is piecewise Lipschitz continuous in the (x, t)plane, and prove the stability (uniqueness) of such entropy solutions, provided that theflux function satisfies a so-called crossng condition, and that strong traces of the solu-tion exist along the curves where k(x, t) is disco 相似文献