Computer implemented techniques for simulating a fluid flow about a surface of a solid are disclosed. These techniques involve receiving a model of a simulation space including a lattice structure represented as a collection of voxels and a representation of a physical object, with the voxels having appropriate resolutions to account for surfaces of the physical object. The techniques also involve simulating movement of particles in a volume of fluid, with the movement of the particles causing collisions among the particles, identifying faces between two voxels where at least one of the faces violates a stability condition, computing a modified flux using a spatially averaged gradient in the vicinity of the two voxels where the at least one of the faces violates the stability condition, and performing by the computing system, advection operations on the particles to subsequent voxels.