Efficient very high-order accurate polyhedral mesh finite volume scheme for 3D conjugate heat transfer problems in curved domains

Abstract

The conjugate heat transfer problem is found in many engineering applications and comprises the heat transfer between solids and fluids in contact. The discretization method of these problems must guarantee that the interface conditions are properly satisfied, which is an additional difficulty when designing a numerical scheme with very high-order of convergence. The three-dimensional case with arbitrary curved domains is particularly challenging to treat, as the standard approaches to preserve the optimal convergence order become cumbersome with the use of curved meshes and non-linear transformations. Moreover, the implementation aspects of very high-order of convergence methods are critical for the three-dimensional case, as the computational cost of conventional algorithms often grows exponentially with the problem dimension. A very high-order accurate finite volume scheme with general polyhedral meshes is proposed in this work, which is able to solve three-dimensional conjugate heat transfer problems in arbitrary curved domains. The implementation of the proposed method is addressed and optimized calculations are derived to provide the same approximate solution at a significantly reduced computational cost. The provided set of numerical benchmarks, addressing several situations of the conjugate heat transfer problem, allows confirming that the optimal convergence order is effectively achieved. The results obtained also show that the proposed method overcomes the main shortcomings of the standard curved mesh approaches, while preserving the accuracy and the convergence order with the sole use of polyhedral meshes. A computational benchmark proves that substantial performance improvements are obtained from the proposed optimization, which represents a significant advance towards less demanding and more efficient numerical simulations.