The high-order spectral volume (SV) method has been extended for solving 3D hyperbolic conservation laws, and its implementation using an efficient quadrature-free approach has been performed to achieve high efficiency while maintaining accuracy. In the SV method, in order to perform a high-order polynomial reconstruction, each simplex cell - called a spectral volume (SV) - is partitioned into a "structured" set of sub-cells called control volumes (CVs) in a geometrically similar manner, thus a universal reconstruction formula can be obtained for all SVs from the cell-averaged solutions on the CVs. The SV method avoids the volume integral required in the DG method, but it does introduce more cell faces where surface integrals are needed. In this paper, the reconstructions for the fluxes are built based on the nodal values on a selected set of optimized and geometrically similar nodes within each SV. The most important advantage of this new approach is to use a set of universal shapefunctions for face integrals, which avoids the use of quadrature formulas without losing the properties of compactness and robustness that are inherent to the SV method. In high-order computations for many practical 3D problems, this new approach greatly reduces the number of computer operations and the required storage as compared to the implementation that uses quadrature formulas. In this paper, accuracy studies are performed on the 3D advection equations, and the 3D Euler equation for vortex evolution problems and flows around a sphere. The designed orders of accuracy have been achieved for all the corresponding orders of polynomial reconstruction.
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