I have question connected with finite volume method. Consider equation$$\frac{\partial u}{\partial t}=\operatorname{div}A\nabla u +f . \quad x\in \overline{B}_{1} (0)\subset \mathbb{R}^3 -\text{unit ball with its boundary}$$ I solved IBVP for this equation with a help of finite volume method, for grid I took uniform spherical coordinates grid,. (picture lower is related to topic)I have a problem with finding flows for the faces of cell: how to approximate the value$$\oint_{\partial V_{i,j,k}}(A\nabla u, n)dS $$(where $A$ is a variable matrix)? When $A$ is an identity matrix everything is clear. Could you help me with this issue or to advise literature where this issue is represented?
Finite volume method
finite volume