In this paper, an improved meshfree scheme based on radial basis functions (RBFs) is present for solving incompressible viscous Navier‐Stokes equations. Two enhancements are proposed to mitigate the numerical oscillations. The first one is the combination of the RBFs‐based finite difference (RBF‐FD) method with the semi‐Lagrangian RBFs (SLM‐RBF), with the former being used for the viscous diffusion

In marine offshore engineering, cost‐efficient simulation of unsteady water waves and their nonlinear interaction with bodies are important to address a broad range of engineering applications at increasing fidelity and scale. We consider a fully nonlinear potential flow (FNPF) model discretized using a Galerkin spectral element method to serve as a basis for handling both wave propagation and wave‐body

In this article, we consider the first‐moment model approximation of the radiative transfer equation. This system is linear hyperbolic and satisfies a diffusion limit. Some finite volume numerical schemes have been proposed which reproduce this diffusion limit [8, 9]. Here, we extend such schemes, originally defined on polygonal meshes, to conical meshes (using rational quadratic Bezier curves). We

This paper discusses a non‐intrusive data‐driven model order reduction method that learns low‐dimensional dynamical models for a parametrized shallow water equation.We consider the shallow water equation in non‐traditional form (NTSWE). We focus on learning low‐dimensional models in a non‐intrusive way. That means, we assume not to have access to a discretized form of the NTSWE in any form. Instead

A novel reduced order model (ROM) for incompressible flows is developed by performing a Galerkin projection based on a fully (space and time) discrete full order model (FOM) formulation. This ‘discretize‐then‐project’ approach requires no pressure stabilization technique (even though the pressure term is present in the ROM) nor a boundary control technique (to impose the boundary conditions at the

In this paper, we present a front capturing method for compressible reactive flows, where a shock tracking technique is applied with level set method. In stiff reaction problems, the difficulty arises when the time scale of the source term is significantly shorter than the time scale of the homogeneous conservation law. The spurious numerical phenomenon may occur due to the smeared out shock profiles

The Cartesian gird has its unique advantages in computational fluid dynamics, especially for complicated boundary cases. However, the main drawback is to resolve the boundary layer structures efficiently and effectively. To overcome such a problem, a new boundary layer structure resolving (BLSR) algorithm is proposed on the basis of the boundary layer physics and force balance analysis. For the present

Achieving high numerical resolution in smooth regions and robustness near discontinuities within a unified framework is the major concern while developing numerical schemes solving hyperbolic conservation laws, for which the essentially non‐oscillatory (ENO) type scheme is a favorable solution. Therefore, an arbitrary‐high‐order ENO‐type framework is designed in this paper. With using a typical five‐point