A sixth-order finite volume method for diffusion problem with curved boundaries

作者：Boularas A; Clain S^*; Baudoin F

来源：Applied Mathematical Modelling, 2017, 42: 401-422.

DOI：10.1016/j.apm.2016.10.004

• Finite volume
• High-order
• Polynomial reconstruction
• Poisson equation
• Curved boundary

A sixth-order finite volume method is proposed to solve the Poisson equation for two and three-dimensional geometries involving Dirichlet condition on curved boundary domains where a new technique is introduced to preserve the sixth-order approximation for non-polygonal or non-polyhedral domains. On the other hand, a specific polynomial reconstruction is used to provide accurate fluxes for elliptic operators even with discontinuous diffusion coefficients. Numerical tests covering a large panel of situations are addressed to assess the performances of the method.

• 出版日期2017-2