Due to improvements in computational resources, interest has recently increased in using implicit scheme for solving flow equations on 3D unstructured grids. However, most of the implicit schemes produce greater numerical diffusion error than their corresponding explicit schemes. This stems from the fact that in linearizing implicit fluxes, it is conventional to replace the Jacobian matrix in t...

We propose a series of techniques for hybridizing implicit and semi-implicit time integration methods in a manner that retains much of the speed of the implicit method without sacrificing all of the higher quality vibrations one obtains with methods that handle elastic forces explicitly. We propose our scheme in the context of asynchronous methods, where different parts of the mesh are evolved ...

Simulations of many rigid bodies colliding with each other sometimes yield particularly interesting results if the objects differ significantly in size and are nonspherical. The most expensive part within such a simulation code is collision detection. We propose family novel multiscale detection algorithms that can be applied to triangulated explicit implicit time stepping methods. They well su...

This work presents, for the first time, a dual time stepping (DTS) approach to solve global system of equations that appears in hybridisable discontinuous Galerkin (HDG) formulation convection-diffusion problems. A proof existence and uniqueness steady state solution HDG problem with DTS is presented. The stability limit derived using von Neumann analysis, leading closed form expression critica...

Implicit-explicit (IMEX) linear multistep methods are examined with respect to their suitability for the integration of fast-wave, slow-wave problems in which the fast wave is physically insignificant and need not be accurately simulated. The widely used combination of trapezoidal implicit and leapfrog explicit differencing is compared to schemes based on 5 Adams methods or on backward differen...

Direct numerical simulation of stability and transition of compressible boundary layers requires high-orderaccurate and computationally efŽ cient numerical methods to resolve a wide range of timeand length scales associated with wave Ž elds in the boundary layers. Explicit methods have been used mainly in such simulations to advance the compressible Navier–Stokes equations in time. However, the...

A fully decoupled, linearized, and unconditionally stable finite element method is developed to solve the Cahn-Hilliard-Navier–Stokes-Darcy model in coupled free fluid region porous medium region. By introducing two auxiliary energy variables, we derive equivalent system that consistent with original system. The dissipation law of proposed proven. To lay a solid foundation, first present linear...