Adaptive Cartesian grids, often accompanied by non-uniform hanging grids, result in non-equidistant node distributions, posing numerical challenges for finite difference discretization. This work introduces a novel cell-based adaptive Cartesian grids solver for compressible flows using a finite difference method, combined with an immersed boundary method to effectively simulate various complex flows. The algorithm selects easily locatable and retrievable neighboring cells around the hanging grid as interpolation templates and employs distance-weighted least squares interpolation to achieve high-precision interpolation. Consequently, equidistant finite difference templates are constructed, enabling high-accuracy finite difference discretization in the transition regions between coarse and fine grids. The advantages of this algorithm include ease of integration with commonly used numerical schemes, flexibility, and implementation convenience. Accuracy tests with the Taylor–Green vortex and vortex convection confirm third-order precision at hanging grids. The algorithm's effectiveness is further demonstrated in laminar flat plate flow, Rayleigh–Taylor instability, cylinder flow, and supersonic flow around a high-aspect-ratio aircraft, showcasing its capability to accurately and efficiently simulate complex flow situations.

The efficient utilization of energy in rich fuel detonation processes and the effective control method of soot are important topics in combustion research. In this paper, we numerically study the detonation wave behavior of acetylene–air systems in rich fuel condition by using a reduced reaction mechanism. The non-stiff terms of the governing equations are solved explicitly using the gas kinetic scheme, and the stiff terms are solved implicitly. Our results show that the acetylene pyrolysis is the dominant reaction process. The oxidation reaction is exploited to initiate the reaction induction process, providing the required energy to overcome the potential energy barrier. The secondary detonation structure is due to the stable interaction of the transverse waves and the combined action of the vinyl reaction system, thus effectively improve the energy release rate and providing a powerful solution for the fuel-rich high-energy release of advanced heat engines. The area of the unreacted pocket increases with the acetylene concentration, resulting in an irregular wave-front and detonation cell. The reflected shock wave impacting on the wall induces the secondary reaction of the detonation products. The concentration of polycyclic aromatic hydrocarbons decreases significantly and regenerates near the wall. Our approach provides an effective tool for controlling detonation soot and the preparation of carbon particles.

With increasing demands for high-fidelity simulations of objects undergoing large-amplitude frequent motions in flow fields, traditional grid-based algorithms face challenges of insufficient computational efficiency and numerical instability. Although non-conformal Cartesian grids combined with immersed boundary methods (IBM) offer automation advantages, their results are still affected by spurious pressure oscillations during the simulation of such motions. To address this issue, we develop a mature dynamic Cartesian grid framework incorporating geometric-adaptive surface tracking and solution-adaptive mesh refinement algorithm. By employing an optimized IBM via the efficient high-fidelity ghost cell approach, integrated with fresh cells treatment for moving objects swept regions, automated high-efficiency simulations of flow fields with moving bodies are achieved. We conducted validations including static and dynamic cylinder flow tests, classic low-Mach number motions, and large-amplitude periodic movements. Through these comparisons with experimental data and high-fidelity computational solutions, we demonstrated that our proposed method significantly outperforms bilinear interpolation in both boundary reconstruction accuracy and overall robustness. This approach enables large-scale simulations of body moving-boundary problems and provides robust support for the rapid design of aerospace vehicles.

Compared to traditional body-fitted moving grids and overset grids, adaptive Cartesian grids offer significant advantages, including no need for grid deformation, highly automated generation process, natural adaptability to complex geometries, and ease of implementing solution-based adaptive mesh refinement. However, in high Reynolds number simulations involving large motions, these grids face the issue of “grid catastrophe” due to the extreme grid resolution required for turbulent boundary layer simulation. To address this, we employ the immersed boundary-dynamic wall function model combined with an implicit dual-time-stepping method, effectively resolving near-wall flow structures without significantly increasing grid count. To handle the assignment of newly emerged Eulerian cells during motion, a three-point interpolation method is used for flow field initialization. This computational framework has been validated through a series of steady-state benchmark cases. Through simulations of typical dive processes and typical pitching airfoil benchmarks, we demonstrate the high efficiency and fidelity of our method in solving turbulent flow fields under dynamic boundary conditions at subsonic and critical sonic speeds. This method provides efficient and reliable numerical simulation support for the aerodynamic design and optimization of various new aircraft.