The results of numerical modeling of white dwarf mergers on massive parallel supercomputers using a AVX-512 technique are presented. A hydrodynamic model of white dwarfs closed by a star equation of state and supplemented by a Poisson equation for the gravitational potential is constructed. This paper presents a modification based on a local linear reconstruction of the solution of the Rusanov scheme for the hydrodynamic equations. This reconstruction makes it possible to considerably decrease the numerical dissipation of the scheme for weak shock waves without any external piecewise polynomial reconstruction. The scheme is efficient for unstructured grids, when it is difficult to construct a piecewise polynomial solution, and also in parallel implementations of structured nested or adaptive grids, when the costs of interprocess interactions increase significantly. As input data, piecewise constant values of the physical variables in the left and right cells of a discontinuity are used. The smoothness of the solution is measured by the discrepancy between the maximum left and right eigenvalues. This discrepancy is used for a local piecewise polynomial reconstruction in the left and right cells. Then the solutions are integrated along the characteristics taking into account the piecewise linear representation of the physical variables. A performance of 234 gigaflops and 33-fold speedup are obtained on two Intel Skylake processors on the cluster NKS-1P of the Siberian Supercomputer Center ICM & MG SB RAS.