Matrix Product State Simulation of Reacting Shear Flows

Accurate simulations of compressible and reacting flows are critical for a wide range of applications. However, such simulations face severe challenges due to the intricacies of exothermicity and turbulence-chemistry interactions. New paradigms of computational fluid dynamics are needed to account for all relevant length and time scales of these flows without incurring the exponential cost of DNS. In this work, a quantum-inspired approach for effectively time-evolving compressible and reacting flows is proposed. The approach is based on a matrix product state (MPS) representation of the governing partial differential equations. This representation correctly captures the physics of the flows, with the potential to significantly reduce computational memory requirements compared to DNS. Simulations of a temporally developing jet are conducted to assess the effects of the Reynolds number, the Mach number, the Damkohler number and the heat release parameter on the flow structure. By encoding DNS results into MPS structures, the level of memory compression required to capture the dynamics of transport variables at high Reynolds numbers is investigated. The conditions for achieving advantage of an MPS representation of transport variable over DNS are identified. This work paves the way for efficient full-scale calculations of complex combustion processes in classical and quantum computing devices.