On the use of composite grid schemes in computational aerodynamics
Computer Methods in Applied Mechanics and Engineering
Numerical computation of internal & external flows: fundamentals of numerical discretization
Numerical computation of internal & external flows: fundamentals of numerical discretization
Finite difference schemes and partial differential equations
Finite difference schemes and partial differential equations
Composite overlapping meshes for the solution of partial differential equations
Journal of Computational Physics
A numerical method to calculate the two-dimensional flow around an underwater obstacle
SIAM Journal on Numerical Analysis
A fourth-order accurate method for the incompressible Navier-Stokes equations on overlapping grids
Journal of Computational Physics
Journal of Computational Physics
Direct simulation of the motion of neutrally buoyant circular cylinders in plane Poiseuille flow
Journal of Computational Physics
An Immersed Interface Method for Incompressible Navier-Stokes Equations
SIAM Journal on Scientific Computing
An adaptive numerical scheme for high-speed reactive flow on overlapping grids
Journal of Computational Physics
An overset-grid method for 3D unsteady incompressible flows
Journal of Computational Physics
A moving overset grid method for interface dynamics applied to non-Newtonian Hele-Shaw flow
Journal of Computational Physics
Journal of Computational Physics
A high-resolution Godunov method for compressible multi-material flow on overlapping grids
Journal of Computational Physics
Journal of Computational Physics
A composite grid solver for conjugate heat transfer in fluid-structure systems
Journal of Computational Physics
An evaluation of the FCT method for high-speed flows on structured overlapping grids
Journal of Computational Physics
A high-resolution mapped grid algorithm for compressible multiphase flow problems
Journal of Computational Physics
Deforming composite grids for solving fluid structure problems
Journal of Computational Physics
Automatic off-body overset adaptive Cartesian mesh method based on an octree approach
Journal of Computational Physics
An adaptive discretization of incompressible flow using a multitude of moving Cartesian grids
Journal of Computational Physics
Richardson Extrapolation for Linearly Degenerate Discontinuities
Journal of Scientific Computing
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We consider the solution of the reactive and non-reactive Euler equations on two-dimensional domains that evolve in time. The domains are discretized using moving overlapping grids. In a typical grid construction, boundary-fitted grids are used to represent moving boundaries, and these grids overlap with stationary background Cartesian grids. Block-structured adaptive mesh refinement (AMR) is used to resolve fine-scale features in the flow such as shocks and detonations. Refinement grids are added to base-level grids according to an estimate of the error, and these refinement grids move with their corresponding base-level grids. The numerical approximation of the governing equations takes place in the parameter space of each component grid which is defined by a mapping from (fixed) parameter space to (moving) physical space. The mapped equations are solved numerically using a second-order extension of Godunov's method. The stiff source term in the reactive case is handled using a Runge-Kutta error-control scheme. We consider cases when the boundaries move according to a prescribed function of time and when the boundaries of embedded bodies move according to the surface stress exerted by the fluid. In the latter case, the Newton-Euler equations describe the motion of the center of mass of the each body and the rotation about it, and these equations are integrated numerically using a second-order predictor-corrector scheme. Numerical boundary conditions at slip walls are described, and numerical results are presented for both reactive and non-reactive flows that demonstrate the use and accuracy of the numerical approach.