Yılmaz Dereli

The meshless kernel-based method of lines for solving the equal width equation

The Equal Width equation governs nonlinear wave phenomena like waves in shallow water. Here, it is solved numerically by the Method of Lines using a somewhat unusual setup. There is no linearization of the nonlinear terms, no error in handling the starting approximation, and there are boundary conditions only at infinity. To achieve a space discretization of high accuracy with only few trial functions, meshless translates of radial kernels are used. In the numerical examples, the motion of solitary waves, the interaction of two and three solitary waves, the generation of wave undulation, the Maxwell initial condition, and the clash of two colliding solitary waves are simulated. Our numerical results compare favourably with results of earlier papers using other techniques.

Numerical solution of RLW equation using radial basis functions

The numerical solution of the regularized long wave equation is investigated by means of the meshless method based on collocation with the well-known radial basis functions (RBFs). Single solitary wave motion, two solitary wave interaction and wave undulation are studied. Results of the meshless method with different RBFs are compared.

Radial basis functions method for numerical solution of the modified equal width equation

The numerical solution of the modified equal width equation is investigated by using meshless method based on collocation with the well-known radial basis functions. Single solitary wave motion, two solitary waves interaction and three solitary waves interaction are studied. Results of the meshless methods with different radial basis functions are presented.

Numerical solutions of the GEW equation using MLS collocation method

In this paper, the generalized equal width wave (GEW) equation is solved by using moving least squares collocation (MLSC) method. To test the accuracy of the method some numerical experiments are presented. The motion of single solitary waves, the interaction of two solitary waves and the Maxwellian initial condition problems are chosen as test problems. For the single solitary wave motion whose analytical solution was known L2, L∞ error norms and pointwise rates of convergence were calculated. Also mass, energy and momentum invariants were calculated for every test problems. Obtained numerical results are compared with some earlier works. It is seen that the method is very efficient and reliable due to obtained numerical results are very satisfactorily. Stability analysis of difference equation was done by applying the moving least squares collocation method for GEW equation.

Rotordynamic coefficients in staggered labyrinth seals

In this paper, the flow properties of staggered labyrinth seals are investigated. Leakage flowrates and pressure distributions are calculated for this seal. Then the dynamic stiffness and damping coefficients are calculated. The results are compared to the results of the some other papers.

Numerical solution of the Rosenau-KdV-RLW equation by using RBFs collocation method

In this study, a meshfree method based on the collocation with radial basis functions (RBFs) is proposed to solve numerically an initial-boundary value problem of Rosenau-KdV-regularized long-wave (RLW) equation. Numerical values of invariants of the motion are computed to examine the fundamental conservative properties of the equation. Computational experiments for the simulation of solitary waves examine the accuracy of the scheme in terms of error norms L2 and L∞. Linear stability analysis is investigated to determine whether the present method is stable or unstable. The scheme gives unconditionally stable, and second-order convergent. The obtained results are compared with analytical solution and some other earlier works in the literature. The presented results indicate the accuracy and efficiency of the method.