A Simple Bound-Preserving Sweeping Technique for Conservative Numerical Approximations
 作者： Yuan Liu,  Yingda Cheng,  Chi-Wang Shu 作者单位： 1Mississippi State University2Michigan State University3Brown University 刊名： Journal of Scientific Computing, 2017, Vol.73 (2-3), pp.1028-1071 来源数据库： Springer Journal DOI： 10.1007/s10915-017-0395-x 关键词： Bound-preserving;  Conservative schemes;  Fourier spectral methods;  High order finite difference and finite volume methods; 英文摘要： In this paper, we propose a simple bound-preserving sweeping procedure for conservative numerical approximations. Conservative schemes are of importance in many applications, yet for high order methods, the numerical solutions do not necessarily satisfy maximum principle. This paper constructs a simple sweeping algorithm to enforce the bound of the solutions. It has a very general framework acting as a postprocessing step accommodating many point-based or cell average-based discretizations. The method is proven to preserve the bounds of the numerical solution while conserving a prescribed quantity designated as a weighted average of values from all points. The technique is demonstrated to work well with a spectral method, high order finite difference and finite volume methods for scalar... conservation laws and incompressible flows. Extensive numerical tests in 1D and 2D are provided to verify the accuracy of the sweeping procedure. 原始语种摘要： In this paper, we propose a simple bound-preserving sweeping procedure for conservative numerical approximations. Conservative schemes are of importance in many applications, yet for high order methods, the numerical solutions do not necessarily satisfy maximum principle. This paper constructs a simple sweeping algorithm to enforce the bound of the solutions. It has a very general framework acting as a postprocessing step accommodating many point-based or cell average-based discretizations. The method is proven to preserve the bounds of the numerical solution while conserving a prescribed quantity designated as a weighted average of values from all points. The technique is demonstrated to work well with a spectral method, high order finite difference and finite volume methods for scalar... conservation laws and incompressible flows. Extensive numerical tests in 1D and 2D are provided to verify the accuracy of the sweeping procedure.

• preserving　保藏
• sweeping　掠过
• bounds　界限
• spectral　谱的
• finite　有限的
• postprocessing　后加工
• procedure　手续
• preserve　保存
• points
• framework　构架