A discrete conservative remapping algorithm based upon refinement and numerical integrals,named particle remapping algorithm,is presented.The mass density distribution is chosen as either a piecewise constant with first-order accuracy or a piecewise linear distribution with second-order accuracy.It results in a first-order and a second-order algorithm.The density gradient is evaluated by an area average method with a piecewise linear distribution.On a staggered mesh,in which velocity is vertex-centered,an auxiliary mesh is introduced,and the velocity is remapped.The particle remapping algorithm can be applied to a structured or an unstructured mesh.It does not require a one-to-one mapping between the old and the new meshes.Numerical results show that the first-order algorithm is robust but has an excessive diffusion.The second-order one is better in shape-preservation but violates the monotonicity sometimes.To improve the monotonicity,a conservative mass repair algorithm for structured grids is extended to unstructured grids preserving upper and lower bounds of the density.Several remapping results are presented and the errors are analyzed.

A new method to generate a quasi-equal distribution of particles on arbitrary domains is provided. Based on an advancing front mesh generation method, triangles are formed at the boundary. These triangle center-points are used for the boundary condition of the Delaunay mesh generation method which generates inward triangles. All vertices of triangles are the particles in meshfree methods. An adaptive method is given to readjust distribution of particles, according to the gradient of fluid density.

The remapping or coupling of physics quantities across different grids occurs when grids are modified or distinct grids are coupled.This paper presents a few remapping algorithms via the strategies of curve fitting and interpolation.The methods are independent of grid type.

The method in computational fluid dynamics requires the periodic remapping of conservation quantities such as mass, momentum, and energy from old or distorted meshes to some other arbitrarily defined meshes. This is a type of interpolation procedure, which is usually constrained to be conservative and monotone. A type of remapping algorithms using spline-approximating methods are presented for numerical simulation codes applied to unstructured or adaptive meshes.