# An open and parallel multiresolution framework using block-based adaptive grids

## TL;DR

This paper introduces a parallel, multiresolution adaptive grid framework for efficiently solving complex PDEs in multiple dimensions, validated on fluid dynamics problems with open-source implementation.

## Contribution

It presents a novel block-based adaptive grid method with multiresolution analysis and parallelization, improving accuracy and efficiency for multi-scale PDE simulations.

## Key findings

- High-order finite difference discretization achieves accurate solutions.
- Parallel implementation with load balancing enhances computational performance.
- Validated on 2D advection and Navier-Stokes equations, demonstrating effectiveness.

## Abstract

A numerical approach for solving evolutionary partial differential equations in two and three space dimensions on block-based adaptive grids is presented. The numerical discretization is based on high-order, central finite-differences and explicit time integration. Grid refinement and coarsening are triggered by multiresolution analysis, i.e. thresholding of wavelet coefficients, which allow controlling the precision of the adaptive approximation of the solution with respect to uniform grid computations. The implementation of the scheme is fully parallel using MPI with a hybrid data structure. Load balancing relies on space filling curves techniques. Validation tests for 2D advection equations allow to assess the precision and performance of the developed code. Computations of the compressible Navier-Stokes equations for a temporally developing 2D mixing layer illustrate the properties of the code for nonlinear multi-scale problems. The code is open source.