Theoretical analysis of the Exponential Transversal Method of Lines for the diffusion equation

Salazar, Abraham J.; Raydan, Marcos; Campo, Antônio

doi:10.1002/(sici)1098-2426(200001)16:1<30::aid-num3>3.0.co;2-v

Cited by 12 publications

(1 citation statement)

References 11 publications

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“…Hybrid combinations are also possible 9 . Other used methods are: transversal methods of lines for the numerical modeling of vertical infiltration into the vadose zone 28 , 29 , or a WENO based method of lines 30 . Although there were very few attempts to use a supercomputer to simulate subsurface solute transport, the situation has changed in the last ten years.. New codes use HPC, for example, PFLOTRAN 31 , 32 , Parflow Hydrologic model 33 , 34 , RichardsFOAM 35 , CATHY (CATchment HYdrology) 36 .…”

Section: High Performance Computing and Cactushydromentioning

confidence: 99%

High-resolution shock-capturing numerical simulations of three-phase immiscible fluids from the unsaturated to the saturated zone

Feo

Celico

2021

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Numerical modeling of immiscible contaminant fluid flow in unsaturated and saturated porous aquifers is of great importance in many scientific fields to properly manage groundwater resources. We present a high-resolution numerical model that simulates three-phase immiscible fluid flow in both unsaturated and saturated zone in a porous aquifer. We use coupled conserved mass equations for each phase and study the dynamics of a multiphase fluid flow as a function of saturation, capillary pressure, permeability, and porosity of the different phases, initial and boundary conditions. To deal with the sharp front originated from the partial differential equations’ nonlinearity and accurately propagate the sharp front of the fluid component, we use a high-resolution shock-capturing method to treat discontinuities due to capillary pressure and permeabilities that depend on the saturation of the three different phases. The main approach to the problem’s numerical solution is based on (full) explicit evolution of the discretized (in-space) variables. Since explicit methods require the time step to be sufficiently small, this condition is very restrictive, particularly for long-time integrations. With the increased computational speed and capacity of today’s multicore computer, it is possible to simulate in detail contaminants’ fate flow using high-performance computing.

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Section: High Performance Computing and Cactushydromentioning

confidence: 99%

High-resolution shock-capturing numerical simulations of three-phase immiscible fluids from the unsaturated to the saturated zone

Feo

Celico

2021

Sci Rep

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An Asymptotic Preserving Maxwell Solver Resulting in the Darwin Limit of Electrodynamics

et al. 2016

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In plasma simulations, where the speed of light divided by a characteristic length is at a much higher frequency than other relevant parameters in the underlying system, such as the plasma frequency, implicit methods begin to play an important role in generating efficient solutions in these multi-scale problems. Under conditions of scale separation, one can rescale Maxwell's equations in such a way as to give a magneto static limit known as the Darwin approximation of electromagnetics.In this work, we present a new approach to solve Maxwell's equations based on a Method of Lines Transpose (MOL T ) formulation, combined with a fast summation method with computational complexity O(N log N ), where N is the number of grid points (particles). Under appropriate scaling, we show that the proposed schemes result in asymptotic preserving methods that can recover the Darwin limit of electrodynamics.

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Kernel Based High Order “Explicit” Unconditionally Stable Scheme for Nonlinear Degenerate Advection-Diffusion Equations

et al. 2020

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In this paper, we present a novel numerical scheme for solving a class of nonlinear degenerate parabolic equations with non-smooth solutions. The proposed method relies on a special kernel based formulation of the solutions found in our early work on the method of lines transpose and successive convolution. In such a framework, a high order weighted essentially non-oscillatory (WENO) methodology and a nonlinear filter are further employed to avoid spurious oscillations. High order accuracy in time is realized by using the high order explicit strong-stability-preserving (SSP) Runge-Kutta method. Moreover, theoretical investigations of the kernel based formulation combined with an explicit SSP method indicates that the combined scheme is unconditionally stable and up to third order accuracy. Evaluation of the kernel based approach is done with a fast O(N ) summation algorithm. The new method allows for much larger time step evolution compared with other explicit schemes with the same order accuracy, leading to remarkable computational savings.

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Theoretical analysis of the Exponential Transversal Method of Lines for the diffusion equation

Cited by 12 publications

References 11 publications

High-resolution shock-capturing numerical simulations of three-phase immiscible fluids from the unsaturated to the saturated zone

High-resolution shock-capturing numerical simulations of three-phase immiscible fluids from the unsaturated to the saturated zone

An Asymptotic Preserving Maxwell Solver Resulting in the Darwin Limit of Electrodynamics

Kernel Based High Order “Explicit” Unconditionally Stable Scheme for Nonlinear Degenerate Advection-Diffusion Equations

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