Hybridizable discontinuous Galerkin reduced order model for the variable coefficient advection equation

In this paper, a hybridizable discontinuous Galerkin (HDG) model order reduction technique is proposed to solve the variable coefficient advection equation. In order to obtain a high precision original full order model (FOM), the HDG and diagonally implicit Runge-Kutta (DIRK) methods are used for space and time discretization, respectively. The obtained FOM can achieve higher order accuracy in both space and time. Then, we introduce POD method and Galerkin projection to construct the reduced order model (ROM). Compared with the FOM, the proposed ROM can maintain the same higher order accuracy and greatly reduce the computational cost. Finally, some numerical results are illustrated to confirm the validity and higher order accuracy of the proposed reduced order HDG method.