APPLYING VARIATIONAL MECHANICS PRINCIPLES TO CONSTRUCTING TIME-DTISCRETE DIFFERENCE MODELS IN GAS DYNAMICS. USING H0L0N0MIC CONNECTIONS TO MAINTAIN DIFFERENCE LAGRANGIAN SCHEME QUALITY

Yu. A. Bondarenko, O. A. Vinokurov
VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki 1988. Вып.2. С. 29-39.

      Vie propose a method to stabilize a difference scheme for 2-D gas dynamics calculations in Lagrangian variables based on using "good" mesh definition (for example, rectangular cell convexity condition) as a holomonic unidirectional connection to be accounted while constructing finite-difference schemes with a time-discrete variational technique. The difference schemes obtained conserve momentum and full energy. Numerical experiments using cell convexity condition showed a good method performance. An obvious method interpretation is presented which allows to use it in difference schemes obtained with other methods.