Related papers: Dimension Splitting and a Long Time-Step Multi-Dim…
We present a parametric family of semi-implicit second order accurate numerical methods for non-conservative and conservative advection equation for which the numerical solutions can be obtained in a fixed number of forward and backward…
We study numerical methods for dissipative particle dynamics (DPD), which is a system of stochastic differential equations and a popular stochastic momentum-conserving thermostat for simulating complex hydrodynamic behavior at mesoscales.…
The term `Convected Scheme' (CS) refers to a family of algorithms, most usually applied to the solution of Boltzmann's equation, which uses a method of characteristics in an integral form to project an initial cell forward to a group of…
This paper is concerned with numerical solution of transport problems in heterogeneous porous media. A semi-discrete continuous-in-time formulation of the linear advection-diffusion equation is obtained by using a mixed hybrid finite…
In this work we study a multi-step scheme on time-space grids proposed by W. Zhao et al. [28] for solving backward stochastic differential equations, where Lagrange interpolating polynomials are used to approximate the time-integrands with…
A new test case is presented for evaluating the compressible dynamical cores of the atmospheric models. The test case is based on a compressible vertical slice model that can be obtained by simple modification of a standard three…
Partitionings (or segmentations) divide a given domain into disjoint connected regions whose union forms again the entire domain. Multi-dimensional partitionings occur, for example, when analyzing parameter spaces of simulation models,…
We introduce a dimensional splitting method based on the intertwining property of the Radon transform, with a particular focus on its applications related to hyperbolic partial differential equations (PDEs). This dimensional splitting has…
The irregular geometry and high inter-slice variability in computerized tomography (CT) scans of the human pancreas make an accurate segmentation of this crucial organ a challenging task for existing data-driven deep learning methods. To…
Active Flux (AF) is a modified Finite Volume method that evolves additional Degrees of Freedom (DoF) located on the cell interfaces to compute high-order approximations to the numerical fluxes through the respective interface. We present an…
A high-order multi-time-step (MTS) scheme for the bond-based peridynamic (PD) model, an extension of classical continuous mechanics widely used for analyzing discontinuous problems like cracks, is proposed. The MTS scheme discretizes the…
In this study, two initial boundary value problems for one dimensional advection-dispersion equation are solved by differential quadrature method based on sine cardinal functions. Pure advection problem modeling transport of conservative…
Nonlinear time fractional partial differential equations are widely used in modeling and simulations. In many applications, there are high contrast changes in media properties. For solving these problems, one often uses coarse spatial grid…
Stochastic models for spatio-temporal transport face a critical trade-off between physical realism and interpretability. The advection model with a single constant velocity is interpretable but physically limited by its perfect correlation…
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.…
Plastic deformation of most crystalline materials is due to the motion of lattice dislocations. Therefore, the simulation of the interaction and dynamics of these defects has become state-of-the-art method to study work hardening, size…
This paper extends the gas-kinetic scheme for one-dimensional inviscid shallow water equations (J. Comput. Phys. 178 (2002), pp. 533-562) to multidimensional gas dynamic equations under gravitational fields. Four important issues in the…
Multidimensional scaling is a statistical process that aims to embed high dimensional data into a lower-dimensional space; this process is often used for the purpose of data visualisation. Common multidimensional scaling algorithms tend to…
Blood flow, dam or ship construction and numerous other problems in biomedical and general engineering involve incompressible flows interacting with elastic structures. Such interactions heavily influence the deformation and stress states…
A new class of asynchronous discrete-event simulation schemes for advection-diffusion-reaction equations are introduced, which is based on the principle of allowing quanta of mass to pass through faces of a Cartesian finite volume grid. The…