各向异性扩散问题Kershaw格式的守恒保正修复算法

针对各向异性扩散方程Kershaw格式的数值解在正交网格及扭曲网格上计算出负的现象，给出一种守恒的保正修复算法（CENZ），该算法对简单遇负置零（ENZ）方法进行改进，使修复后的数值解不仅具有非负性，而且保持法向通量的局部守恒性.数值算例表明，该方法不受计算网格类型和扩散系数各向异性比的限制，可用于对任意违背单调性（或保正性）的有限体积格式数值解的修复.

Conservative Positivity-Preserving Algorithm for Kershaw Scheme of Anisotropic Diffusion Problems

Kershaw scheme is not positivity-preserving. Negative values emerge in numerical simulation for anisotropic diffusion equations on both orthogonal and distorted meshes. A conservative enforcing negative value to zero(CENZ) algorithm is proposed, which is an improvement of traditional method. It not only repairs numerical solution nonnegative, but also keeps local conservation of energy fluxes. Numerical examples demonstrate that the method is not limited by anisotropic ratio of diffusion coefficients. The algorithm can be used for numerical solution of finite volume schemes which violate monotony or positivity-preserving.