Abstract
An alternative formulation of targeted ENO scheme (AFTENO) is proposed for hyperbolic conservation laws. The new scheme combines the advantages of targeted ENO (TENO) and the alternative formulation of weighted essentially non-oscillatory scheme (AFWENO). AFTENO has more flexible characteristics than the original TENO. For instance, the former can use the TENO interpolation algorithm directly to interpolate conserved variables, primitive variables, and physical flux. AFTENO can use the arbitrary monotone flux function to construct numerical fluxes, while TENO can only reconstruct the smooth flux splitting function. Similar to TENO, AFTENO also adopts the design strategy of gradually increasing the width of the candidate stencil, which can avoid scheme failure caused by multiple discontinuities in the global stencil. Compared with AFWENO, which only has odd order accuracy, AFTENO can achieve arbitrary high-order accuracy. The performance of AFTENO is tested by a series of one-dimensional (1D) and two-dimensional (2D) cases, e.g., the 1D blast wave interaction and 2D Rayleigh Taylor instability. All numerical tests suggest that AFTENO can deal with strong discontinuities robustly and achieve low dissipation.
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