We use the finite volumes method with wights model to solve the problem by using splitting  by physical characteristics  we get an easier version to solve this problem algorithmically.

We further reduce the  arithmetical process by getting some of parts as implicit. Test the algorithm against the solution of "Течение Пуазейля в трубе или в канале" try and solve "квадратная каверна с движущейся крышкой" add the heat equation to problem  try and solve " квадратная каверна с движущейся крышкой  "  with the heat equations.