Second and higher order numerical approximations of conservation laws for vector fields
call for the use of limiting techniques based on generalized monotonicity criteria. In this …

The role of entropy for the stability of hyperbolic conservation laws is well-understood, and to
some extent, also for first-and second-order accurate numerical schemes. The stability of …

Existing entropy-consistent Euler flux avoids spurious oscillations and exactly preserves the
stationary contact discontinuity but still leaves much room for further improvement in …

Many processes in nature, physics, and other application fields can be described by
mathematical models based on partial differential equations (PDEs). Variables of these …

提出了一种求解浅水波方程组的熵相容格式. 在熵稳定通量中添加特征速度差分绝对值的项来
抵消解在跨过激波时所产生的熵增, 从而实现熵相容. 新的数值差分格式具有形式简单 …

格式和高阶熵守恒格式结合, 具有熵守恒格式和熵稳定格式的优点: 在解的光滑区域具有高精度,
在解的间断区域避免了非物理现象的产生, 同时可以准确地捕捉激波, 从而达到高分辨率的效果 …

针对带源项的底部非平坦浅水波方程, 本文对高阶紧致中心加权基本无振荡(CCWENO)
型熵稳定格式的保平衡性进行研究, 证明了格式的保平衡性, 通过一维和二维数值算例进行验证 …

针对浅水波方程, 提出了一类低耗散基本无振荡熵稳定格式. 在Roe 型熵稳定通量中添加熵守恒
格式的熵数值黏性绝对值的量来抵消解在跨过激波时所产生的熵增, 从而抑制伪振荡; 并且 …

We review the currently available stability properties of the essentially nonoscillatory
reconstruction procedure, such as its monotonicity and nonoscillatory properties, the sign …

The shallow water equations with source term have steady-state solution. The numerical
scheme for solving this kind of equations must have well-balanced property, otherwise it will …