This paper examines the behavior of flux and slope limiters on non - uniform grids in multiple dimensions . We note that on non - uniform grids the scalar formulation in standard use today sacrifices k - exactness , even for linear solutions , impacting both accuracy and convergence . We rewrite some well - known limiters in a n way to highlight their underlying symmetry , and use this to examine both traditional and novel limiter formulations . A consistent method of handling stretched meshes is developed , as is a new directional formulation in multiple dimensions for irregular grids . Results are presented demonstrating improved accuracy and convergence using a combination of model problems and complex three - dimensional examples .