Numerical simulation of Suliciu relaxation model via an mR scheme

We suggest a group of reliable and efficient finite volume techniques for solving the Suliciu relaxation model numerically. Namely, we have developed the modified Rusanov (mR) method to solve this model. This system is divided into two parts, the first of which is dependent on a local parameter that allows for diffusion control. The conservation equation is recovered in stage two. One of the key characteristics of the mR scheme is its ability to calculate the numerical flux equivalent to the solution's real state in the absence of the Riemann solution. Several numerical examples are considered. These examples indicate the mR scheme's high resolution and highlight its ability to deliver correct results for the Suliciu relaxation model. A variety of additional models in developed physics and applied science can be solved by using the mR method.