In this paper, a new direct vertex-centred finite volume method (CV-FEM) has been developed for the thermoelastic problem in functional graded material (FGM) based on Lord-Shulman theory. The heat conduction equation in Lord-Shulman theory is modified by considering the product term of spatial gradient of relaxation time and the heat flux rate, and it makes the present method more accurate to capture characteristics of a thermoelastic wave in inhomogeneous and FGM compared with previous methods. Some benchmark examples are used to demonstrate the capability of the present method for hyperbolic heat conduction and thermoelastic coupled problems. The effects of the ‘product-term’ on the wave propagation are studied by a heat conduction problem in inhomogeneous material and a thermoelastic problem in FGM. The FGM results show that its effect on the thermoelastic response is significant even for a linear variation of material properties.
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