The purpose of this study is to determine what finite-difference algorithms are best used in numerical simulation of two-dimensional single-phase saturated porous media flows when the models have a nondiagonal symmetric tenser for the mobility (or hydraulic conductivity) that has nontrivial jump discontinuities along lines that are not aligned with the coordinate axes. Such problems arise naturally in many modeling situations and, in addition, when simpler problems are studied using adaptive grids. The answer is surprising, the simplest finite-difference method, called the MAC Scheme with Linear Averaging, performs nearly as well as most other algorithms over a wide range of problems. A new algorithm, called the Full Harmonic Averaged Scheme, is significantly more costly to use, but does perform better than the simplest scheme in certain interesting cases. The simplest finite-difference method is compared to some finite-element simulations taken from the literature; the finite-difference algorithm performs better. Many of the conclusions of the paper rest on testing the algorithms on a new class of problems with analytic solutions. The problems have a nondiagonal mobility tenser and can have a jump discontinuity of arbitrary height.