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A fourth-order finite volume embedded boundary (EB) method is presented for the unsteady Stokes equations. The algorithm represents complex geometries on a Cartesian grid using EB, employing a technique to mitigate the ``small cut-cell"" problem without mesh modifications, cell merging, or state redistribution. Spatial discretizations are based on a weighted least-squares technique that has been extended to fourth-order operators and boundary conditions, including an approximate projection to enforce the divergence-free constraint. Solutions are advanced in time using a fourth-order additive implicit-explicit Runge-Kutta method, with the viscous and source terms treated implicitly and explicitly, respectively. Formal accuracy of the method is demonstrated with several grid convergence studies, and results are shown for an application with a complex bio-inspired material. The developed method achieves fourth-order accuracy and is stable despite the pervasive small cells arising from complex geometries.

A new adaptive clipping-and-redistribution method is presented which provides bounds-preservation for multidimensional interpolation in the context of high-order finite-volume discretizations with adaptive mesh refinement (AMR). The underlying finite-volume method (FVM) for the computational fluid dynamics applications is fourth-order accurate for smooth solutions and utilizes AMR for computational efficiency in solving multiscale problems involving turbulence and combustion. High-order interpolation between different AMR levels is required. However, this operation often leads to numerical issues because combustion species must have physical bounds preserved. The present study overcomes two major challenges in the development of the high-order interpolation method. First, the method needs to be bound-preserving near extrema or discontinuities to prevent the emergence of unphysical oscillations while maintaining fourth-order accuracy in smooth flows. Second, the method needs to satisfy the conservation requirement in multiple dimensions, particularly in the context of curvilinear coordinate transformations. Additionally, the method is designed to be localized and computationally inexpensive. The new interpolation scheme is demonstrated by solving reacting flows, which are extremely sensitive to unphysical overshoots in conserved quantities. The test problems are shock-induced (Formula presented.) - (Formula presented.) combustion and a (Formula presented.) -air flame in a practical bluff-body combustor. Results show the method prevents new extrema near discontinuities while maintaining high-order accuracy in smooth regions. In particular, the method is extremely beneficial for combustion with stiff chemistry. With the proposed new method, even if flame fronts cross AMR interfaces or new grids are created in the vicinity of the flame, solution stability is retained.

Photochemical dearomative cycloaddition has emerged as a useful strategy to rapidly generate molecular complexity. Within this context, stereo- and regiocontrolled intermolecular para-cycloadditions are rare. Herein, a method to achieve photochemical cycloaddition of quinolines and alkenes is shown. Emphasis is placed on generating sterically congested products and reaction of highly substituted alkenes and allenes. In addition, the mechanistic details of the process are studied, which revealed a reversible radical addition and a selectivity-determining radical recombination. The regio- and stereochemical outcome of the reaction is also rationalized.

In this paper, we present components of a fourth-order finite volume method that will eventually allow for solving the incompressible Navier-Stokes equations. The algorithm represents complex geometries on a Cartesian embedded boundary grid, and takes special steps to achieve stable and accurate discretizations. Spatial discretizations are based on a weighted least-squares technique that mitigates the “small cut cell” problem, without mesh modifications, cell merging, or redistribution. Solutions are advanced in time using a projection method coupled with a higher-order additive implicit-explicit (ImEx) Runge-Kutta method, where the diffusion and advection terms are treated implicitly and explicitly, respectively. We demonstrate convergence tests for a scalar advection-diffusion equation and an approximate projection solver and confirm fourth-order accuracy for complex geometries. These methods are key components of solvers for the incompressible Navier-Stokes equations, and indicate feasibility of achieving higher-order accuracy on an arbitrary cut cell mesh.

Simulations of complex, compressible, high-Reynolds-number flows require high-fidelity physics and turbulence models to be appropriately coupled with strong numerical regularization methods. Obtaining grid-independent and scheme-independent solutions of these flows when using both explicit turbulence models and additional numerical regularization is especially important for further testing and development of accurate physics models. To this end, the current study investigates the interaction between the stretched-vortex subgrid-scale model and both the fourth-order piecewise parabolic limiter and a fifth-order upwinding interpolation (or hyperviscosity). It is demonstrated that computing the subgrid-scale kinetic energy estimate for the stretched-vortex model at a coarser resolution than the base mesh provides results which are independent of the use of numerical regularization techniques. This is shown to be the case for a temporally-evolving shear-layer, the inviscid Taylor–Green vortex problem, and a decaying, homogeneous turbulent flow.

A fourth-order accurate finite-volume method is presented for solving time-dependent hyperbolic systems of conservation laws on mapped grids that are adaptively refined in space and time. Novel considerations for formulating the semi-discrete system of equations in computational space are combined with detailed mechanisms for accommodating the adapting grids. These considerations ensure that conservation is maintained and that the divergence of a constant vector field is always zero (freestream-preservation property). The solution in time is advanced with a fourth-order Runge-Kutta method. A series of tests verifies that the expected accuracy is achieved in smooth flows and the solution of a Mach reflection problem demonstrates the effectiveness of the algorithm in resolving strong discontinuities.