A DIFFERENCE SCHEME WITH NONLINEAR ARTIFICIAL VISCOSITY

V. V. Bashurov, A. E. Ushakov
VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki 1984. Вып.3. С. 19-24.

      A difference scheme for solving a transport equation with a nonlinear dissipative function (the so called D-viscosity) is examined. The difference equation is studied by the first difference approximation. Linearizing the first difference approximation in the vicinity of a partial solution gave uncertainty growth and its second derivative estimates. The artificial dissipative term (D-viscosity) is shown to correct the oscillations occrurring before they become fully grown and degrade the solution.