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Recent decades are put lots of efforts to develop a higher-order scheme forconvective terms approximation that is stable and reliable. The idea presentedhere is that approximation approach has to correspond to the physicalphenomenon described by approximated terms. Pure convection (advection) that isdescribed by convective terms is transporting a property along the streamline,and the information propagation is unidirectional, i.e., transported propertydepends on previous values along the streamline but does not depend on the nextones. The proposed approach represents streamlines on mesh as discretestreamlines and is called Discrete Stream(line) Method (DStreaM). A discretestreamline here is represented as a narrow triangle with one vertex of theapproximated node and two others neighbor upstream nodes. Discrete streamlinesare orientated using local flow direction as skew upwind schemes. DStreaMcorresponds to pure convection. Here are considered standard test problems:advection of a step profile, advection of a double-step profile, advection of asinusoidal profile, and Smith and Hutton problem. DStreaM solutions werecompared with upwind-first order scheme and second-order Total VariationDiminishing (TVD) schemes with limiters Min-Mod, QUICK, and SUPERBEE solutions.DStreaM demonstrated second-order accuracy and rapid convergence. Upwind andDStreaM need 2 or 4 iterations to reach a final solution while TVD schemes needfrom 15 to 93.5 more iterations. DStreaM approach looks promising forcalculation of convective-dominated problems because it approximates naturallyfirst derivatives and is straightforwardly applicable as a meshfree method oron unstructured meshes.

On convective terms approximation approach that corresponds to pure convection