Space-time adaptive numerical methods for geophysical applications.

Area of Science:

• Computational physics
• Numerical analysis
• Geophysics

Background:

• Accurate simulation of wave propagation is crucial for geophysical applications like tsunami and seismic wave analysis.
• Traditional methods often face challenges with computational cost and accuracy trade-offs, especially on unstructured meshes.
• Existing techniques may not efficiently handle varying wave speeds or optimize computational resources.

Purpose of the Study:

• To develop and present high-order formulations for finite volume and discontinuous Galerkin methods for wave propagation.
• To implement a space-time adaptation technique using unstructured meshes to reduce computational expense.
• To enhance accuracy and efficiency in simulating geophysical wave phenomena.

Main Methods:

• High-order spatial polynomials and a high-order solution of the generalized Riemann problem are employed.
• A high-order time integration method based on Taylor series expansion is utilized.
• Static adaptation with locally refined meshes and locally adaptive time stepping based on stability criteria are implemented.

Main Results:

• The study validates the numerical approach through application to geophysical wave propagation problems (tsunami, seismic waves).
• Comparison with classical global time-stepping techniques demonstrates improved efficiency and accuracy.
• A novel mesh partitioning approach is proposed and tested for large-scale, multi-processor applications.

Conclusions:

• The presented high-order finite volume and discontinuous Galerkin methods with space-time adaptation offer a computationally efficient and accurate solution for wave propagation.
• The adaptive strategies effectively manage computational resources and improve approximation quality.
• The proposed mesh partitioning method further enhances scalability and reduces computational cost for large-scale simulations.