A SIMPLE NUMERICAL SCHEME FOR THE COMPUTATION OF RESONANT ALFVEN WAVES

The present paper discusses the implementation of the SGHR method (Sakurai, Goossens, and Hollweg, 1991; Goossens, Ruderman, and Hollweg, 1995) in a numerical scheme for determining resonantly driven Alfven waves in nonuniform magnetic flux tubes. This method is based on jump conditions over the dissipative layer which are obtained from an asymptotic analysis of analytical solutions to simplified versions of the linear non-ideal MHD equations in this dissipative layer. The emphasis is on the computational simplicity and the accuracy of the method. The method derives its computational simplicity from the fact that it circumvents the numerical integration of the nonideal MHD equations. The implementation only requires the numerical integration of the ideal MHD equations away from the resonant position. There is no need for a special integration scheme and a PC suffices as a hardware tool. The accuracy of the method is verified by means of test computations. These test computations deal with the loss of power of acoustic waves in sunspots by resonant absorption of Alfven waves. Results for the absorption coefficients obtained with the SGHR method are compared with known results in the literature obtained by integration of the full set of the linearized non-ideal MHD equations. The agreement is excellent and identifies the SGHR method as a powerful and extremely easy to use tool for studying resonant Alfven waves.