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This paper proposes a new approach for solving partial differential equations related to fluid problems. The technique merges two methods: the variational numerical method and the multi-grid technique. The modified variational numerical method with a grid refinement module is used to solve physical equations by finding the action minimum on a coarse grid and interpolating it to finer grids, with reduced computer work on the finer grid while achieving the same accuracy. The interpolation computer work can be performed efficiently and therefore may be neglected compared with the time invested in the variation solution itself. The current work analyses the effect of algorithm parameters such as the number of levels, the required accuracy and the type of grid point.

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