中文摘要：

这篇论文为非线性的夸张能量守恒定律和密切相关的传送对流散开方程论述高分辨率本地人时间步计划的一个类，由投射在每本地时间步的内在的部分微分方程(PDE ) 的解决方案增长。主要优点是他们一致性好，并且实现他们是方便的。计划是 L~ ∞马厩，满足房间熵不平等，并且可以被扩大到有高顺序的空间衍生物的一般不稳定的 PDE 的起始的边界价值问题。高分辨率计划被分别地把重建技术与第二个顺序 TVD Runge-Kutta 计划或一个 Lax-Wendroff 类型方法相结合给。计划被用来解决一个线性传送对流散开方程，非线性的在里面胶粘的汉堡包的方程， theone 维、二维的可压缩的 Euler 方程，和二维的 incompressibleNavier 司烧方程。数字结果证明计划具有高顺序的精确性，并且在节省特别，为联合的盒子，礼品与适应网孔方法策划的计算费用有效。慢动人或更强壮的断绝的正确地点也被获得，尽管计划是稍微非保守的。

英文摘要：

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.