Local multiquadric RBF meshless scheme for radiative heat transfer in strongly inhomogeneous media

- A local RBF meshless method is developed to solve radiative transfer problems.
- Multiquadric (MQ) RBF is employed to construct the trial functions.
- An upwind support domain scheme is introduced to improve numerical stability.
- Radiative transfer in strongly inhomogeneous media is investigated.
- The upwind local MQ RBF meshless method can achieve high accuracy and stability.

A local radial basis function meshless method (LRBFM) is developed to solve radiative heat transfer in participating media, in which multiquadric (MQ) radial basis functions (RBF) augmented with polynomial basis are employed to construct the trial functions, and the radiative transfer equation (RTE) is discretized directly at nodes by collocation method. The LRBFM belongs to a class of truly meshless methods which do not need any mesh, and can be implemented on a set of uniform or irregular nodes without nodes׳ connectivity. To improve numerical stability of LRBFM for the solution to radiative heat transfer in strongly inhomogeneous media, an upwind support domain scheme is introduced. The upwind scheme is implemented by moving the support domain of local radial basis function interpolation approximation to the opposite direction of each streamline, which can fully capture the information from upstream and improve the accuracy and stability of LRBFM. Performances of the LRBFM and upwind LRBFM (LRBFM_U) are compared with analytical solutions and other numerical results reported earlier in the literatures via a variety of problems in 1-D and 2-D geometries with strongly inhomogeneous media. It is demonstrated that the local radial basis function meshless method with upwind support domain scheme (LRBFM_U) provides high accuracy and great stability to solve radiative heat transfer in strongly inhomogeneous media.