A Positivity-Preserving Finite Volume Scheme for Heat Conduction Equation on Generalized Polyhedral Meshes

The positivity‐preserving finite volume scheme with fixed stencils for anisotropic diffusion problems on general polyhedral meshes

“…$$ The homogeneous Dirichlet boundary condition $$$ {g}_D=0 $$$ is imposed on $$$ \mathrm{\partial \Omega } $$$. This test is a typical problem of testing positivity, which has been used in Reference 17 and 18. Although there is no analytical solution, according to the maximum principle, we know that the true solution must be nonnegative.…”

“…In 2017, Wang 17 considered the nonplanar cell‐face of the mesh and proposed a PPFV scheme based on the effective directional flux, and the algorithm to calculate vertex unknowns is based on harmonic averaging points. In 2018, Xie 18 extended the PPFV scheme proposed by Sheng and Yuan 19 in 2016 to polyhedral meshes. In addition, in 2018, Wang and Hang 17 proposed a positivity‐preserving pyramid scheme(P‐scheme), which is designed for polyhedral cells with nonplanar cell‐faces.…”

The positivity‐preserving finite volume scheme with fixed stencils for anisotropic diffusion problems on general polyhedral meshes

“…$$ The homogeneous Dirichlet boundary condition $$$ {g}_D=0 $$$ is imposed on $$$ \mathrm{\partial \Omega } $$$. This test is a typical problem of testing positivity, which has been used in References 17 and 18. Although there is no analytical solution, according to the maximum principle, we know that the true solution must be nonnegative.…”

“…In 2017, Wang 17 considered the nonplanar cell‐face of the mesh and proposed a PPFV scheme based on the effective directional flux, and the algorithm to calculate vertex unknowns is based on harmonic averaging points. In 2018, Xie 18 extended the PPFV scheme proposed by Sheng and Yuan 19 in 2016 to polyhedral meshes. In addition, in 2018, Wang and Hang 20 proposed a positivity‐preserving pyramid scheme(P‐scheme), which is designed for polyhedral cells with nonplanar cell‐faces.…”