Room acoustics modelling in the time-domain with the nodal discontinuous Galerkin method

Abstract

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An arbitrary high-order discontinuous Galerkin method with local time-stepping for linear acoustic wave propagation

“…To avoid redundant repetitions with previous works 50 while introducing necessary notations for the convenience of discussion, first, we briefly review the main ingredients of the nodal DG method, which is used for the spatial discretization. Acoustic wave propagation can be described by the following coupled system of linear acoustic equations:…”

“…The resulting vector-matrix form of the formulation and additional descriptions of implementations can be found in Ref. 50.…”

Dissipation-free and dispersion-optimized explicit time-domain finite element method for room acoustic modeling

“…Developments of FEM-based room acoustic solvers in both the frequency-domain [1,2] and time-domain [3][4][5][6][7][8][9][10][11][12][13] are active research areas in recent years. Actually, FEM is attractive for room acoustic modeling because of its outstanding potential in modeling arbitrarily shaped rooms and various acoustical materials accurately.…”

“…However, the hp-FEM, the SEM and the DGFEM use the combination of h-refinement and p-refinement, known as hp-refinement, reducing the dispersion error with an exponential rate. Recent works [7][8][9]13] have applied SEM and the nodal DGFEM to room acoustic problems, presenting their applicability in room acoustics modeling including both frequency-independent and frequency-dependent impedance boundaries. These higher-order FEMs can generally conduct acoustic simulations with fewer computational costs than the linear FEM because the use of higher-order polynomials can reduce the degrees of freedom (DOF) to achieve a similar level of accuracy.…”

Potential of Room Acoustic Solver with Plane-Wave Enriched Finite Element Method

“…The finite element method (FEM) [1][2][3][4][5], boundary element method (BEM) [6], and finite difference time domain (FDTD) [7][8][9] method exemplify the often-used numerical methods for room acoustic simulations. Although they entail a huge computational effort for acoustic simulations especially at kilohertz frequencies in a real-sized room, their application to room acoustics prediction is increasing gradually by virtue of the progress of computer technology and the continuous development of efficient methods [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24]. In addition, some recent studies [16,18,22,25] use extended-reaction boundary conditions to address both the frequency dependent and incident-angle dependent absorption characteristics of sound absorbers accurately, whereas many studies use the simplest local-reaction boundary conditions, which simplify the incident-angle dependence of surface impedance.…”