A numerical model for solving the linearized gravity-wave equations by a multilayer method

Abstract. We developed a numerical model to solve the linearized gravity-wave equations by a multilayer approach. Specifically, the model handles the linearized equations including viscosity, thermal conduction, and ion drag. The solution methods are based on the matrix exponential formalism and encompass two main approaches: (i) global matrix methods and (ii) scattering matrix methods. Both methods are focused on determining either (i) the amplitudes of the characteristic solutions or (ii) the discrete values of the solution vector. Ascending and descending wave modes are distinguished based on the criterion that the real parts of the eigenvalues of the characteristic equation for ascending modes are smaller than those for descending modes. In global matrix methods, ascending and descending modes can be defined (i) at the upper and lower boundaries or (ii) in each layer. In contrast, scattering matrix methods necessitate explicitly determining the mode type within each layer. The model accommodates two types of lower boundary conditions and can handle both single-frequency waves and time wavepackets. Our simulations demonstrate that the solution methods are numerically stable and achieve comparable accuracies. Among them, the global matrix method for computing the amplitudes of the characteristic solutions is the most efficient.