A method of adaptive artificial viscosity for solving numerically the equations of a viscous heat-conducting compressible gas

Статья посвящена численному решению уравнений динамики вязкого сжимаемого теплопроводного газа на неструктурированных тетраэдальных сетках. Предложена комбинация методов МакКормака и Лакса-Вендроффа, которая позволяет провести приближенную монотонизацию разностной схемы с помощью введения адаптивной искусственной вязкости и метода "замороженных" коэффициентов. Результаты расчетов согласуются с натурными экспериментами. This paper is devoted to the numerical solution of the dynamics equations for a viscous heat-conducting compressible gas by the method of adaptive viscosity on unstructured tetrahedral meshes. A combination of the MacCormack method and the Lax-Wendroff method allows one to monotonize the difference scheme using the method of frozen coefficients. The numerical results are in good agreement with experimental data.

A hybrid approach for the regularized long wave-Burgers equation

In this paper, a new hybrid approach based on sixth-order finite difference and seventh-order weighted essentially non-oscillatory finite difference scheme is proposed to capture numerical simulation of the regularized long wave-Burgers equation which represents a balance relation among dissipation, dispersion and nonlinearity. The corresponding approach is implemented to the spatial derivatives and then MacCormack method is used for the resulting system. Some test problems discussed by different researchers are considered to apply the suggested method. The produced results are compared with some earlier studies, and to validate the accuracy and efficiency of the method, some error norms are computed. The obtained solutions are in good agreement with the literature. Furthermore, the accuracy of the method is higher than some previous works when some error norms are taken into consideration.

Numerical Treatment of a Modified MacCormack Scheme in a Nondimensional Form of the Water Quality Models in a Nonuniform Flow Stream

Two mathematical models are used to simulate water quality in a nonuniform flow stream. The first model is the hydrodynamic model that provides the velocity field and the elevation of water. The second model is the dispersion model that provides the pollutant concentration field. Both models are formulated in one-dimensional equations. The traditional Crank-Nicolson method is also used in the hydrodynamic model. At each step, the flow velocity fields calculated from the first model are the input into the second model as the field data. A modified MacCormack method is subsequently employed in the second model. This paper proposes a simply remarkable alteration to the MacCormack method so as to make it more accurate without any significant loss of computational efficiency. The results obtained indicate that the proposed modified MacCormack scheme does improve the prediction accuracy compared to that of the traditional MacCormack method.