Adaptive local grid refinement and multi-grid in numerical reservoir simulation
Journal of Computational Physics
Local adaptive mesh refinement for shock hydrodynamics
Journal of Computational Physics
Towards the ultimate conservative difference scheme V. A second-order sequel to Godunov's method
Journal of Computational Physics - Special issue: commenoration of the 30th anniversary
Adaptive mesh refinement and multilevel iteration for flow in porous media
Journal of Computational Physics
On the Choice of Wavespeeds for the HLLC Riemann Solver
SIAM Journal on Scientific Computing
An efficient shock-capturing algorithm for compressible multicomponent problems
Journal of Computational Physics
Adaptive Mesh Refinement Using Wave-Propagation Algorithms for Hyperbolic Systems
SIAM Journal on Numerical Analysis
An r-adaptive finite element method based upon moving mesh PDEs
Journal of Computational Physics
Conservative smoothing on an adaptive quadrilateral grid
Journal of Computational Physics
Journal of Computational Physics
Computations of compressible multifluids
Journal of Computational Physics
Moving mesh methods in multiple dimensions based on harmonic maps
Journal of Computational Physics
A five-equation model for the simulation of interfaces between compressible fluids
Journal of Computational Physics
A Cartesian grid method with transient anisotropic adaptation
Journal of Computational Physics
Error localization in solution-adaptive grid methods
Journal of Computational Physics
Gerris: a tree-based adaptive solver for the incompressible Euler equations in complex geometries
Journal of Computational Physics
Journal of Computational Physics
Adaptive characteristics-based matching for compressible multifluid dynamics
Journal of Computational Physics
Implementation of WENO schemes in compressible multicomponent flow problems
Journal of Computational Physics
A high-resolution Godunov method for compressible multi-material flow on overlapping grids
Journal of Computational Physics
A high-resolution mapped grid algorithm for compressible multiphase flow problems
Journal of Computational Physics
Hi-index | 31.45 |
In this paper, an object-oriented and quadrilateral-mesh based solution adaptive algorithm for the simulation of compressible multi-fluid flows is presented. The HLLC scheme (Harten, Lax and van Leer approximate Riemann solver with the Contact wave restored) is extended to adaptively solve the compressible multi-fluid flows under complex geometry on unstructured mesh. It is also extended to the second-order of accuracy by using MUSCL extrapolation. The node, edge and cell are arranged in such an object-oriented manner that each of them inherits from a basic object. A home-made double link list is designed to manage these objects so that the inserting of new objects and removing of the existing objects (nodes, edges and cells) are independent of the number of objects and only of the complexity of O(1). In addition, the cells with different levels are further stored in different lists. This avoids the recursive calculation of solution of mother (non-leaf) cells. Thus, high efficiency is obtained due to these features. Besides, as compared to other cell-edge adaptive methods, the separation of nodes would reduce the memory requirement of redundant nodes, especially in the cases where the level number is large or the space dimension is three. Five two-dimensional examples are used to examine its performance. These examples include vortex evolution problem, interface only problem under structured mesh and unstructured mesh, bubble explosion under the water, bubble-shock interaction, and shock-interface interaction inside the cylindrical vessel. Numerical results indicate that there is no oscillation of pressure and velocity across the interface and it is feasible to apply it to solve compressible multi-fluid flows with large density ratio (1000) and strong shock wave (the pressure ratio is 10,000) interaction with the interface.