Pseudospectral solution of linear evolution equations of second order in space and time on unstructured quadrilateral subdomain topologies

Aerodynamic and aeroacoustic analysis of a pulsating internal flow by a multidomain weak collocation spectral method

“…This is efficiently accomplished by decomposing the continuous problem into a series of elliptic kernels to be sequentially solved at every discrete time level. Furthermore, an option between an implicit Newmark scheme and an explicit Runge-Kutta-Nyström method is offered for the time integration of the wave evolution system (Kondaxakis and Tsangaris, 2005). A weak formulation of the influence matrix method as well as a combination of the LU factorization algorithm and of the matrix diagonalization technique are employed for the efficient solution of the linear algebraic systems of discrete equations which arise after the full discretization of each problem.…”

“…The low resolution numerical computation was characterized by the parameters N f = 8, t f = 10 −2 , N w =7 and t w =2×10 −2 , the medium resolution calculation by N f =N w =9 and t f = t w =10 −3 , while the high resolution simulation used the numerical values N f = 10, t f = 10 −4 , N w = 11 and t w =5×10 −5 . Furthermore, we should add that for the low resolution solution of the pressure perturbation the classic Newmark time integration method was utilized, for the medium resolution computation the modified version of the same algorithm (Kondaxakis and Tsangaris, 2005), while for the high resolution calculation theRunge-Kutta-Nyström methodology was, naturally, selected for the accurate numerical simulation of the wave field.…”

“…with d a , d b ∈ R real constants to be subsequently commented on and with the scalar functions and appropriately defined in Kondaxakis and Tsangaris (2005). Let us mention that the function indicates the curvature of the section of the computational border on which Robin boundary conditions are imposed (refer to Antoine and Barucq, 1999 for general formulations), while is utilized to represent the so-called sponge function.…”

“…Specifically, we utilized the parameters N w = 23 and t w = 10 −3 , N w = 25 and t w = 5 × 10 −4 , as well as N w = 27 along with t w = 2.5 × 10 −4 , for the degree of the polynomial approximations of the acoustic pressure disturbance function and for the time step of the temporal discretization of the system of differential equations, respectively, for the low, medium, and high resolution simulations. We are obliged to add that at the higher resolution calculations, the modified formulation of the Newmark algorithm was employed (see Kondaxakis and Tsangaris, 2005), so as to prevent a possible unacceptable increase of the roundoff error due to the usage of a particularly small time step. Figs.…”