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The development of a class of low-diffusion upwinding methods for computing dense gas–solid flows is presented in this work. An artificial compressibility/low-Mach preconditioning strategy is developed for a hyperbolic two-phase flow equation system consisting of separate solids and gas momentum and continuity equations. The eigenvalues of this system are used to devise extensions of the AUSM+ and LDFSS flux-splitting methods that provide high resolution capturing of bubble growth and collapse in gas–solid fluidized beds. Applications to several problems in fluidization are presented. [Copyright &y& Elsevier]