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This paper presents a novel adaptive-sparse polynomial dimensional decomposition (PDD) method for stochastic design optimization of complex systems. The method entails an adaptive-sparse PDD approximation of a high-dimensional stochastic…
A general, compact way of achieving second-order in finite-volume numerical methods is to perform a MUSCL-like, piecewise linear reconstruction of flow properties at each cell interface. To avoid the surge of spurious oscillations in the…
We consider iterative methods for solving the linearised Navier-Stokes equations arising from two-phase flow problems and the efficient preconditioning of such systems when using mixed finite element methods. Our target application is…
In this contribution we present a local discontinuous Galerkin (LDG) pressure-correction scheme for the incompressible Navier-Stokes equations. The scheme does not need penalty parameters and satisfies the discrete continuity equation…
The constrained transport (CT) method reflects the state of the art numerical technique for preserving the divergence-free condition of magnetic field to machine accuracy in multi-dimensional MHD simulations performed with Godunov-type, or…
High-order reconstruction schemes for the solution of hyperbolic conservation laws in orthogonal curvilinear coordinates are revised in the finite volume approach. The formulation employs a piecewise polynomial approximation to the…
This paper develops a shock capturing approach for high-order correction procedure via reconstruction (CPR) method with Legendre-Gauss solution points. Shock regions are treated by novel compact nonuniform nonlinear weighted (CNNW) schemes,…
The paper proposes a physically consistent numerical discretization approach for simulating viscous compressible multicomponent flows. It has two main contributions. First, a contact discontinuity (and material interface) detector is…
The use of limiting methods for high-order numerical approximations of hyperbolic conservation laws generally requires defining an admissible region/bounds for the solution. In this work, we present a novel approach for computing solution…
The two promising methods for capturing high-speed flows are local artificial diffusivity (LAD) and centralised gradient-based reconstruction (C-GBR), the former being computationally economical and the latter being more robust and stable…
This study proposes an extension of the high-order compact gas-kinetic scheme (CGKS) to compressible flow simulation in an arbitrary Lagrangian-Eulerian (ALE) formulation in unstructured mesh. The ALE method is achieved by subdividing…
The compact scheme has high order accuracy and high resolution, but cannot be used to capture the shock. WENO is a great scheme for shock capturing, but is too dissipative for turbulence and small length scales. We developed a modified…
The goal of this study is to develop an efficient numerical algorithm applicable to a wide range of compressible multicomponent flows. Although many highly efficient algorithms have been proposed for simulating each type of the flows, the…
The smoothed particle hydrodynamics (SPH) method has been widely used to simulate incompressible and slightly compressible fluid flows. Adaptive refinement strategies to dynamically increase the resolution of the particles to capture sharp…
A numerical analysis of the effect of artificial viscosity is undertaken in order to understand the effect of numerical diffusion on numerical boundary feedback control. The analysis is undertaken on the linear hyperbolic systems…
This paper presents an extension of the hybrid scheme proposed by Wang et al. (J. Comput. Phys. 229 (2010) 169-180) for numerical simulation of compressible isotropic turbulence to flows with higher turbulent Mach numbers. The scheme still…
Adaptive control strategies usually are designed based on gradient methods for the sake of simplicity in Lyapunov analysis. However, least squares (LS)-based parameter identifiers, with proper selection of design parameters, exhibit better…
High resolution, non-oscillatory, central difference (NOCD) numerical schemes are introduced as alternatives to more traditional artificial viscosity (AV) and Godunov methods for solving the fully general relativistic hydrodynamics…
Dynamical low-rank (DLR) approximation has gained interest in recent years as a viable solution to the curse of dimensionality in the numerical solution of kinetic equations including the Boltzmann and Vlasov equations. These methods…
This paper serves to treat boundary conditions numerically with high order accuracy in order to match the two-stage fourth-order finite volume schemes for hyperbolic problems developed in [{\em J. Li and Z. Du, A two-stage fourth order…