Validation suite for numerical solvers calculating effective thermal conductivity in porous media

Abstract

A validation suite for numerical solvers calculating effective thermal conductivity in porous media is presented. In a first step an appropriate numerical solver based on the finite volume method is developed. Subsequently validation is done with six benchmark cases. The benchmarks are grouped in one-dimensional and three-dimensional problems. Each group includes one case with homogeneous material, one case with function-graded material and one case with heterogeneous material. Building on that, five application cases will be examined. The cases can be grouped in two academic problems and three real world rock samples. During the validation process the focus is set on two main questions. Firstly, how to ensure the quality of numerical results? Secondly, how do different interpolation techniques for the determination of interfacial conductivity influence numerical results? In general extensive use of mesh refinement studies is made. With a maximum relative error of 25% between coarsest possible mesh and expected converged solution, it is shown that refinement studies are an important step towards numerical quality control. Further it is observed, that step-wise defined thermal conductivities, as it is the case in porous media, might lower the theoretical order of accuracy of a given numerical scheme.