Using the Discrete Wavelet Transform for Lossy On‐the‐Fly Compression of <scp>GPU</scp> Fluid Simulations

ABSTRACT High‐performance computing in fluid dynamics frequently confronts substantial memory demands, especially in large‐scale applications. Data compression techniques can alleviate these memory constraints, but introduce new challenges. This paper introduces an innovative on‐the‐fly low‐overhead lossy compression technique tailored for GPU‐based fluid simulations, utilizing the discrete wavelet transform (DWT). The technique is applicable to any numerical scheme where the data is stored on a regular grid and the time step is computed using a stencil. Our approach significantly diminishes memory requirements, achieving up to a 10‐fold long‐term reduction on a D3Q27 simulation, while minimally impacting the simulation accuracy. The methodology is built around careful design choices to achieve a satisfactory compression ratio/speed trade‐off. It effectively maintains mass conservation and accurately preserves essential discontinuities in simulations. Extensive testing with a D3Q27 Lattice‐Boltzmann method (LBM) simulation on a single GPU has shown that large‐scale grids can be processed with minimal impact on the simulation accuracy and acceptable compression times. This compression technique demonstrates a robust capability to handle memory limitations in fluid simulations, opening the door to more complex and larger‐scale simulations.