  Applying the concept of S-convergence, based on averaging in the spirit of
Strong Law of Large Numbers, the vanishing viscosity solutions of the Euler
system are studied. We show how to efficiently compute a viscosity solution of
the Euler system as the S-limit of numerical solutions obtained by the
Viscosity Finite Volume method. Theoretical results are illustrated by
numerical simulations of the Kelvin--Helmholtz instability problem.
