IntrodutionThe space-time conservation element and solution element (CE/SE) method is a high-resolution and genuinely multidimensional method for solving conservation laws . Its nontraditional features include: (i) a unified treatment of space and time; (ii) the introduction of conservation elements (CEs) and solution elements (SEs) as the vehicles for enforcing space-time flux conservation; (iii) a novel time marching strategy that has a space-time staggered stencil at its core and, as such, fluxes at an interface can be evaluated without using any interpolation or extrapolation procedure (which, in turn, leads to the method's ability to capture shocks without using Riemann solvers); (iv) the requirement that each scheme be built from a non-dissipative core scheme and, as a result, the numerical dissipation can be controlled effectively; and (v) the fact that mesh values of the physical dependent variables and their spatial derivatives are considered as independent marching variables to be solve for simultaneously. Note that CEs are nonoverlapping space-time subdomains introduced such that (i) the computational domain can be filled by these subdomains; and (ii) flux conservation can be enforced over each of them and also over the union of any combination of them. On the other hand, SEs are space-time subdomains introduced such that (i) the boundary of each CE can be divided into several component parts with each of them belonging to a unique SE; and (ii) within a SE, any physical flux vector is approximated using simple smooth functions. In general, a CE does not coincide with a SE.Without using flux-splitting or other special techniques, since its inception [1] the unstructured-mesh compatible CE/SE method has been used to obtain numerous accurate 1D, 2D and 3D steady and unsteady flow solutions with Mach numbers ranging from 0.0028 to 10 [42]. The phyical phenomena modeled include traveling and interacting shocks, acoustic waves, shedding vortices, viscous flows, detonation waves, cavitation, flows in fluid film bearings, heat conduction with melting and/or freezing, electrodynamics, MHD vortex, hydraulic jump, crystal growth, and chromatographic problems . In particular, the rather unique capability of the CE/SE method to resolve both strong shocks and small disturbances (e.g., acoustic waves) simultaneously [11,13,14] makes it an effective tool for attacking computational aeroacoustics (CAA) problems. Note that the fact that second-order CE/SE schemes can solve CAA problems accurately is an exception to the commonly-held belief that a second-order scheme is not adequate for solving CAA problems. Also note that, while numerical dissipation is needed for shock capturing, it may also result in annihilation of small disturbances. Thus a solver that can handle both strong shocks and small disturbances simultaneously must be able to overcome this difficulty.In spite of its past successes, there is still room for improving the CE/SE method. An example is the fact that, in a CE/SE simulation with a fixed t...