Related papers: Implicit gradients based conservative numerical sc…
A low diffusive flux difference splitting based kinetic scheme is developed based on a discrete velocity Boltzmann equation, with a novel three velocity model. While two discrete velocities are used for upwinding, the third discrete…
Many engineering applications can be formulated as optimizations constrained by conservation laws. Such optimizations can be efficiently solved by the adjoint method, which computes the gradient of the objective to the design variables.…
In order to prevent velocity, pressure, and temperature spikes at material discontinuities occurring when the interface-capturing schemes inconsistently simulate compressible multi-material flows(when the specific heats ratio is…
Fluid flows are omnipresent in nature and engineering disciplines. The reliable computation of fluids has been a long-lasting challenge due to nonlinear interactions over multiple spatio-temporal scales. The compressible Navier-Stokes…
The ability to differentiate through optimization problems has unlocked numerous applications, from optimization-based layers in machine learning models to complex design problems formulated as bilevel programs. It has been shown that…
We introduce a second-order numerical scheme for compressible atmospheric motions at small to planetary scales. The collocated finite volume method treats the advection of mass, momentum, and mass-weighted potential temperature in…
High-speed turbulent flows are encountered in most space-related applications (including exploration, tourism and defense fields) and represent a subject of growing interest in the last decades. A major challenge in performing high-fidelity…
This paper proposes a new non-oscillatory {\em energy-splitting} conservative algorithm for computing multi-fluid flows in the Eulerian framework. In comparison with existing multi-fluid algorithms in literatures, it is shown that the mass…
In this article, we propose a novel conservative diffuse-interface method for the simulation of immiscible compressible two-phase flows. The proposed method discretely conserves the mass of each phase, momentum and total energy of the…
We present numerical simulations of diffusio-osmotic flow, i.e. the fluid flow generated by a concentration gradient along a solid-fluid interface. In our study, we compare a number of distinct approaches that have been proposed for…
A computationally accurate and efficient numerical method under a unified framework is crucial to various multi-scale scientific and engineering problems. So far, many numerical methods have encountered various challenges in efficiently…
High-order implicit shock tracking (fitting) is a class of high-order, optimization-based numerical methods to approximate solutions of conservation laws with non-smooth features by aligning elements of the computational mesh with…
We extend the shifted boundary method (SBM) to the simulation of incompressible fluid flow using immersed octree meshes. Previous work on SBM for fluid flow primarily utilized two- or three-dimensional unstructured tetrahedral grids.…
In this paper, a novel immersed boundary method is developed, validated, and applied. Through devising a second-order three-step flow reconstruction scheme, the proposed method is able to enforce the Dirichlet, Neumann, Robin, and Cauchy…
Simulating infiltration in porous media using Richards' equation remains computationally challenging due to its parabolic structure and nonlinear coefficients. While a wide range of numerical methods for differential equations have been…
In this exploratory study, we apply shock-capturing schemes within the framework of the Particles on Demand kinetic model to simulate compressible flows with mild and strong shock waves and discontinuities. The model is based on the…
This study proposes an algorithm for modeling compressible flows in spherical shells in nearly incompressible and weakly compressible regimes based on an implicit direction splitting approach. The method retains theoretically expected…
This work introduces an optimization-based $rp$-adaptive numerical method to approximate solutions of viscous, shock-dominated flows using implicit shock tracking and a high-order discontinuous Galerkin discretization on traditionally…
We present direct methods and symbolic software for the computation of conservation laws of nonlinear partial differential equations (PDEs) and differential-difference equations (DDEs).The methods are applied to nonlinear PDEs in (1+1)…
The Immersed Boundary Method (IBM) is one of the popular one-fluid mixed Eulerian-Lagrangian methods to simulate motion of droplets. While the treatment of a moving complex boundary is an extremely time consuming and formidable task in a…