Developments in Cartesian cut cell methods
Mathematics and Computers in Simulation - MODELLING 2001 - Second IMACS conference on mathematical modelling and computational methods in mechanics, physics, biomechanics and geodynamics
ADER schemes for three-dimensional non-linear hyperbolic systems
Journal of Computational Physics
A direct Eulerian GRP scheme for compressible fluid flows
Journal of Computational Physics
Effects of direction decoupling in flux calculation in finite volume solvers
Journal of Computational Physics
An improved Quiet Direct Simulation method for Eulerian fluids using a second-order scheme
Journal of Computational Physics
Compact third-order limiter functions for finite volume methods
Journal of Computational Physics
An adaptive GRP scheme for compressible fluid flows
Journal of Computational Physics
Hi-index | 31.45 |
The integral form of the conventional HLL fluxes are presented by taking integrals around the control volume centred on each cell interface. These integrals are demonstrated to reduce to the conventional HLL flux through simplification by assuming spatially constant conserved properties. The integral flux expressions are then modified by permitting the analytical inclusion of spatially linearly varying conserved quantities. The newly obtained fluxes (which are named HLLG fluxes for clarification, where G stands for gradient inclusion) demonstrate that conventional reconstructions at cell interfaces are invalid and can produce unstable results when applied to conventional HLL schemes. The HLLG method is then applied to the solution of the Euler Equations and Shallow Water Equations for various common benchmark problems and finally applied to a 1D fluid modeling for an argon RF discharge at low pressure. Results show that the correct inclusion of flow gradients is shown to demonstrate superior transient behavior when compared to the existing HLL solver and conventional spatial reconstruction without significantly increasing computational expense.