Topic
Finite difference method
About: Finite difference method is a research topic. Over the lifetime, 21603 publications have been published within this topic receiving 468852 citations. The topic is also known as: Finite-difference methods & FDM.
Papers published on a yearly basis
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Papers
TL;DR: In this paper, an implicit finite difference method for the multidimensional Stefan problem is discussed, where the classical problem with discontinuous enthalpy is replaced by an approximate Stefan problem with continuous piecewise linear enthpy.
Abstract: An implicit finite difference method for the multidimensional Stefan problem is discussed. The classical problem with discontinuous enthalpy is replaced by an approximate Stefan problem with continuous piecewise linear enthalpy. An implicit time approximation reduces this formulation to a sequence of monotone elliptic problems which are solved by finite difference techniques. It is shown that the resulting nonlinear algebraic equations are solvable with a Gauss-Seidel method and that the discretized solution converges to the unique weak solution of the Stefan problem as the time and space mesh size approaches zero.
149 citations
TL;DR: An explicit symmetric linear phase-fitted four-step method with a free coefficient as parameter used for the optimization of the method in order to solve efficiently the Schrodinger equation and related oscillatory problems is developed.
149 citations
TL;DR: In this article, a method for simulating incompressible, imiscible, unsteady, Newtonian, multi-fluid flows with free surfaces is described, where a sharp interface separates fluids of different density and viscosity.
148 citations
TL;DR: In this article, a Dirichlet boundary value problem for a delay parabolic differential equation is studied on a rectangular domain in the x-t plane, where the second-order space derivative is multiplied by a small singular perturbation parameter, which gives rise to parabolic boundary layers on the two lateral sides of the rectangle.
147 citations
TL;DR: In this article, numerical solutions to the equation for advection under conditions that permit an analytic solution are calculated using various finite-difference approximations, and their accuracy is investigated by comparison with the analytic solution.
Abstract: Numerical solutions to the equation for advection under conditions that permit an analytic solution are calculated using various finite-difference approximations, and their accuracy is investigated by comparison with the analytic solution. It is shown that upstream differencing introduces a pseudo-diffusive effect that is about as large as the effect of the turbulent diffusion modeled in typical small-scale circulation simulation; hence, the numerical solution is rendered inconsistent with the differential equation. In the solutions obtained with centered-difference schemes, an anomalous oscillation is present when the grid-spacing is too large to follow very closely the variations of the quantity being advected. This oscillation leads to inaccuracy and numerical instability. Of all the schemes investigated, only the Roberts-Weiss approximation advected the initial distribution correctly, but this scheme required about 10–40 times as much computer time as any of the other schemes.
147 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 53 |
| 2024 | 136 |
| 2023 | 170 |
| 2022 | 357 |
| 2021 | 733 |
| 2020 | 690 |