High-Order Approximations for a Pseudoparabolic Equation of Turbulent Mass-Transfer Diffusion

Numerical solutions of turbulent mass-transfer diffusion present challenges due to the nonlinearity of the elliptic–parabolic degeneracy of the mathematical models. Our main result in this paper concerns the development and implementation of an efficient high-order numerical method that is fourth-order accurate in space and second-order accurate in time for computing both the solution and its gradient for a Barenblatt-type equation. First, we reduce the original Neumann boundary value problem to a Dirichlet problem for the equation of the solution gradient. This problem is then solved by a compact fourth-order spatial approximation. To implement the numerical discretization, we employ Newton’s iterative method. Then, we compute the original solution while preserving the order of convergence. Numerical test results confirm the efficiency and accuracy of the proposed numerical scheme.