A convection-diffusion equation is discretized by a finite volume method in two space dimensions. The grid is partitioned into blocks with jumps in the grid size at the block interfaces. Interpolation in the cells adjacent to the interfaces is necessary to be able to apply the difference stencils. Second order accuracy is achieved and the stability of the discretizations is investigated. The interface treatment is tested in the solution of the compressible Navier-Stokes equations. The conclusions from the scalar equation are valid also for these equations.
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