Based on a second-order accurate linear scheme, a normal flux is reconstructed to obtain a nonlinear finite volume scheme with a two-point flux discrete stencil on tetrahedral meshes. It is suitable for discontinuous and anisotropic diffusion coefficient problems, and can be generalized to general polyhedral meshes. It is unnecessary to assume that auxiliary unknowns are non-negative, and avoids artificial processing of "setting negative to be zero" in calculating auxiliary unknowns. Moreover, it is proved that the linearized scheme at each nonlinear iteration step satisfies strong positivity-preserving, i.e., as the source term and boundary condition are non-negative, non-zero solution of the scheme is strictly greater than zero. Numerical tests verify that the scheme has second-order accuracy and is strong positivity-preserving.

Radiative transfer in fluid flow of radiation hydrodynamics is studied.Kinetic laws under radiation condition are investigated.Practical radiation hydrodynamics process is complicated,and numerical simulation is one of primary research means.Splitting methods are often used in numerical simulation,in which fluid motion and radiation are computed separately.We discuss computational problems in radiation diffusion calculations.Diffusion schemes and nonlinear iterative methods on severely distorted meshes are studied.A brief introduction on research progress is given.

With special control volumes and finite volume element spaces,two symmetry-preserving finite volume element schemes for stationary diffusion problems are established on unstructured quadrilateral grids.Saturated order of error in L²-norm and H¹-norm for discrete solutions under quasi-uniform partition is demonstrated as diffusion coefficient is smooth.Numerical examples verify theoretical results.It shows strong adaptability of the scheme on distorted quadrilateral grids and for diffusion problems with non-smooth coefficient.The second scheme shows super-approximation for flux function at central point of element as grids are orthogonal.