Calculation of impurity propagation in laminar flow of incompressible fluid inside a diffuser and comparison of performance of some calculation schemes

This study develops and tests a new finite-difference scheme named the TIIAME NRU scheme. It focuses on modeling impurity transport in laminar flows of incompressible fluids within diffusers. This approach addresses the conservativity loss issues seen in older numerical methods. The methodology focused on creating the TIIAME NRU scheme. This was done by strictly following the laws of mass and momentum conservation. It was compared to the classical Courant-Isaacson-Rees scheme. This was done through numerical tests on problems with known solutions in two-dimensional diffusers. Four cases were analyzed: incompressible flow in an expanding diffuser; compressible medium flow; variable cross-section flow; axisymmetric problems in cylindrical coordinates. The findings indicate that the proposed TIIAME NRU scheme demonstrates superior performance in maintaining conservativity, particularly in complex geometries with velocity sign changes. The new scheme remains stable with 15-20% larger time steps without accuracy loss, maintains strict conservation laws even under compressible flow conditions, and shows invariance to coordinate system choice. Numerical experiments confirmed that the classical scheme loses conservativity when impurity flows collide or merge, while the TIIAME NRU scheme preserves mass conservation. In conclusion, the TIIAME NRU scheme provides a robust solution for impurity transport calculations in complex geometries, offering improved stability and conservativity over traditional methods, and can be extended to three-dimensional problems with minimal algorithmic modifications. The practical implications of this research are significant for applications in jet engine design, gas burner optimization, and power plant calculations, where accurate impurity transport modeling is critical, and its improved computational efficiency and stability make it suitable for integration into industrial CFD packages.