A locally-adaptive truly-explicit time-marching formulation for acoustic analyses

Resumo

This study discusses a novel explicit time-marching procedure for solving acoustic problems in the time domain. The procedure is designed to adapt to the characteristics of the spatially discretized model, providing a fully automated and highly effective solution. The approach is second-order accurate, explicitly formulated, and self-starting, offering the advantages of adaptive algorithmic dissipation and extended stability limits. Furthermore, the paper discusses automated subdomain/sub-cycling splitting procedures that enhance the performance of the proposed formulation. By partitioning the model domain into multiple subdomains based on
the discretization properties, different time-step values can be utilized to ensure stability and enable more precise and efficient analyses. The method incorporates adaptive values for the time integration parameters, which are determined based on the characteristics of the spatial discretization. This locally-defined self-adjustable formulation establishes a link between the spatial and temporal solution procedures, better compensating for their errors. The paper presents and discusses expressions for the adaptive time integration parameters and the limiting time-step values of the discretized domain elements. Finally, numerical results are presented at the end of the paper, comparing them to those obtained using standard techniques, thereby illustrating the performance of the discussed approach.