In this work a robust discontinuous Galerkin (DG) solver for turbulent high-lift aerodynamic flows using the turbulence model of Spalart and Allmaras (SA) is developed. The application of DG discretizations to turbulent RANS flows is one of the most pressing issues facing high-order methods on unstructured grids. The issue is the result of non-smooth behavior of the turbulence model equation, w...

‎we describe the construction of second derivative general linear methods (sglms) of orders five and six‎. ‎we will aim for methods which are a--stable and have runge--kutta stability property‎. ‎some numerical results are given to show the efficiency of the constructed methods in solving stiff initial value problems‎.

In some previous works, two of the authors introduced a technique to design high-order numerical methods for one-dimensional balance laws that preserve all their stationary solutions. The basis these is well-balanced reconstruction operator. Moreover, they procedure modify any standard operator, like MUSCL, ENO, CWENO, etc., in order be well-balanced. This strategy involves non-linear problem a...

Predictor-corrector (PC) methods for the numerical solution of stiff ODEs can be extended to include the second derivative of the solution. In this paper, we consider second derivative PC methods with the three-step second derivative Adams-Bashforth as predictor and two-step second derivative Adams-Moulton as corrector which both methods have order six. Implementation of the proposed PC method ...

‎In this paper a new family of fifteenth-order methods with high efficiency index is presented‎. This family include four evaluations of the function and one evaluation of its first derivative per iteration.‎ ‎Therefore‎, ‎this family of methods has the efficiency index which equals 1.71877‎. ‎In order to show the applicability and validity of the class‎, ‎some numerical examples are discussed‎.

in this paper high order multidimensional positive definite advection transport algorithm (mpdata) and compact finite difference methods are applied to one (1-d) and two-dimensional (2-d) advection equation. mpdata methods are designed based on upwind scheme using anti-diffusive velocity that compensates diffusivity of upwind method. in high order compact method one implicit relation between a ...