Related papers: High order compact schemes for flux type BCs
This article aims at developing a high order pressure-based solver for the solution of the 3D compressible Navier-Stokes system at all Mach numbers. We propose a cell-centered discretization of the governing equations that splits the fluxes…
Numerical simulation of multi-component flow systems characterized by the simultaneous presence of pressure-velocity coupling and pressure-density coupling dominated regions remains a significant challenge in computational fluid dynamics.…
In this work, we design and analyze a Hybrid High-Order (HHO) discretization method for incompressible flows of non-Newtonian fluids with power-like convective behaviour. We work under general assumptions on the viscosity and convection…
High order accurate Hermite methods for the wave equation on curvilinear domains are presented. Boundaries are treated using centered compatibility conditions rather than more standard one-sided approximations. Both first-order-in-time…
We present a unified hard-constraint framework for solving geometrically complex PDEs with neural networks, where the most commonly used Dirichlet, Neumann, and Robin boundary conditions (BCs) are considered. Specifically, we first…
This paper presents hybrid numerical techniques for solving the Boltzmann transport equation formulated by means of low-order equations for angular moments of the angular flux. The moment equations are derived by the projection operator…
Efficient performance of a number of engineering systems is achieved through different modes of operation - yielding systems described as "hybrid", containing both real-valued and discrete decision variables. Prominent examples of such…
The recent approach based on Hamiltonian systems and the implicit parametri\-za\-tion theorem, provides a general fixed domain approximation method in shape optimization problems, using optimal control theory. In previous works, we have…
We present a new higher-order accurate finite difference explicit jump Immersed Interface Method (HEJIIM) for solving two-dimensional elliptic problems with singular source and discontinuous coefficients in the irregular region on a compact…
Based on our recent results, in this paper, a compact finite difference scheme is derived for a time fractional differential equation subject to the Neumann boundary conditions. The proposed scheme is second order accurate in time and…
This work introduces a new higher-order super-compact (HOSC) implicit finite difference scheme for analyzing three-dimensional (3D) natural convection and entropy generation in non-Newtonian fluids. The proposed scheme achieves fourth-order…
The diffuse-domain, or smoothed boundary, method is an attractive approach for solving partial differential equations in complex geometries because of its simplicity and flexibility. In this method the complex geometry is embedded into a…
In this work, fourth-order compact block-centered finite difference (CBCFD) schemes combined with the Crank-Nicolson discretization are constructed and analyzed for solving parabolic integro-differential type non-Fickian flows in…
An automatically differentiable, high-order non-oscillatory finite volume shallow water dynamic core has been constructed on a cubed sphere grid. This dynamic core has four advantageous properties: high order accuracy, essential…
We present a novel efficient implementation of the flexible boundary condition (FBC) method, initially proposed by Sinclair et al., for large single-periodic problems. Efficiency is primarily achieved by constructing a hierarchical matrix…
It is well known that multigrid methods are optimally efficient for solution of elliptic equations (O(N)), which means that effort is proportional to the number of points at which the solution is evaluated). Thus this is an ideal method to…
Higher-order numerical methods are used to find accurate numerical solutions to hyperbolic partial differential equations and equations of transport type. Limiting is required to either converge to the correct type of solution or to adhere…
While various parameterizations of vertical turbulent fluxes at different levels of complexity have been proposed, each has its own limitations. For example, simple first-order closure schemes such as the K-Profile Parameterization (KPP)…
In this article, we design and analyze a Hybrid High-Order (HHO) finite element approximation for a class of strongly nonlinear boundary value problems. We consider an HHO discretization for a suitable linearized problem and show its…
We present a high-order compact finite difference approach for a class of parabolic partial differential equations with time and space dependent coefficients as well as with mixed second-order derivative terms in $n$ spatial dimensions.…