Abstract: A new method for numerical modelling of aquatic environments is presented in this paper. It is based on a hybrid method of fractional steps using triangular grids and with L_∞-stability, An upwind discretization scheme or a modified characteristics procedurs is used for convection operator,the lumping finite element technique for diffusion calculation. Stability analysis proved in detail shows that the scheme is L_∞-stable under conditions. (1)Δ≤min((2d)/v,(d²)/(3k)) where V=max√u²+v², d=the minimum perpendicular length of all the triangles, k=diffusivity,and(2)all the angles of triangles are less than or equal to π/2.It is shown also that the L∞-stability implies the nonnegativity of numerical solutions for the concentration or for the excess temperature. To test numerically the convergence and accuracy of this method for nonlinear problem the method was run for a one-dimenslonal nonlinear convection diffusion equation with known analybic soluticn.It can be concluded that the numerical damping effect in computation is insignificant,the modified characteristics procedure for treatment of the convection has more accuracy than the upwind scheme. L∞-stability, simplicity and flexibility in handling complex geometries make this method applicable to many practical problems.