Methods and apparatus for fast computation of fluid velocity fields in the presence of objects causing flow discontinuity are disclosed. Rigorous evaluation of perturbed velocity fields, each resulting from placing an object in a bounded space sustaining a reference velocity field, are determined for different orientations of the object with respect to a reference velocity field and different values of the magnitude of the velocity field. A velocity field is determined at selected sampling points within an enclosure surrounding the object. Pre-computed perturbed velocity fields determined for each object of a set of reference objects are stored in a computer memory. Fast real-time computation of velocity-field perturbations caused by presence of objects at arbitrary positions in a space sustaining velocity fields of different magnitudes and directions are realized using the stored pre-computed data.