Implicit, high-resolution, compact schemes for gas dynamics and aeroacoustics

implicit, high-order schemes are developed for time-accurate numerical solu tions of hyperbolic equation systems. High-order spatial accuracy for the i mplicit operators is obtained at no additional computing cost by performing compact differentiation. The resulting alternating direction implicit and unfactored algorithms yield improved dispersion characteristics compared to second-order accurate in space implicit schemes which makes them suitable for high-resolution numerical simulations in gas dynamics and computational aeroacoustics. First, a fourth-order accurate in space implicit, factorize d scheme, which requires block-tridiagonal matrix inversion, is presented. Next, a class of implicit factorized schemes, which require scalar matrix i nversions, is presented. Higher order of accuracy in space of the implicit operators is achieved at the expense of inverting sc alar matrices with lar ger bandwidth. Finally, extensions to unfactored algorithms, which use upwi nd compact schemes, are obtained. The proposed high-order schemes can be im plemented with little modification of existing second-order accurate in spa ce, implicit CFD methods. The efficiency, accuracy, and convergence charact eristics of the new, high-resolution implicit schemes are demonstrated by t heir implementation for test problems. (C) 1999 Academic Press.