## 1 Introduction  
Under the dominance of second order accurate methods in computational fluid dynamics (CFD) for real applications, the discontinuous Galerkin (DG) method started becoming increasingly popular in recent years due to its ability to achieve higher order spatial accuracy rigorously, even on an unstructured grid [1; 2; 3; 4]. The compressible DG method is used in a wide spectrum of flow regimes [5; 6; 7; 8; 9; 10]. In order to be able to capture shocks existing in the flow fields, several key ingredients, such as slope limiter [5], weighted essentially non-oscillatory (WENO) based limiter [6; 7], and artificial viscosity [8; 9] are usually imposed. The application of the slope limiter requires the identification of the elements lying in the shock region, and also requires for the reduction of the interpolating polynomial to be first order in those identified elements, which may destroy the high-order accuracy in the shocked region. In order to maintain the required accuracy, a WENO-based limiter can be selected at the cost of high computational time consuming. In contrast, the artificial viscosity-based approach is reported to be efficient in view of a relatively low cost [8] and to be flexible in terms of independence on the approximation order with different types of mesh elements [9]. Thus, in the present work, artificial viscosity is intended to be imposed on the preconditioned DG method, capable of compressible shocked flow simulations with explicit or implicit time integration schemes. In general, the schemes with implicit time integration have the advantage of the time steps not being restricted by the severely strict stability limits in comparison to the explicit counterpart [2; 10], and hence so-called implicit acceleration can often be achieved in terms of the convergence rate. In fact, successful efforts and applications were reported usingclassical implicit schemes, including the generalized minimal residual method [11; 12; 13], implicit Runge-Kutta method [3; 14] and the lower-upper symmetric Gauss-Seidel (LU-SGS) method [15] etc. In contrast, an LU-based implicit scheme is proven to be robust in calculations over a wide range of Mach numbers [16]. However, for the flows over aerodynamic bodies at low Mach numbers [17; 10; 18; 19], the undesirable effects, such as low convergence speed (stiffness problem [10; 19]) and loss of accuracy (reaching unphysical solution [18]), may appear due to the large disparity of wave speeds of the governing equations. Such effects are reported to be greatly ameliorated through adopting techniques such as preconditioning [19]. It can be learned that most previous research concerning the preconditioned DG method are focused on the flows at low Mach numbers without the presence of shock waves. This paper presents an effort to develop a high-order accurate DG method with the key ingredients of preconditioning and shock capturing, capable of both nearly incompressible and compressible transonic shocked flow simulations. The preconditioning is realized by multiplying a matrix of the type of Weiss and Smith to the time derivative of the Euler equations, and the shock capturing ability is then enforced through adding an artificial viscosity term to the right side of the resulting preconditioned Euler equations. A detailed description is given of the DG spatial discretization scheme employed, with particular emphasis on the proposed treatment of curved boundaries through adopting a non-uniform rational basis spline (NURBS) surface equipped with a radial basis function (RBF) interpolation to propagate the boundary curve fit motion to the interior of the mesh. An explicit Runge-Kutta scheme associated with time integration is first applied to update the solutions, and the implicit counterpart is then formed through adopting the LU-SGS algorithm.