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Register a new userExtrapolated DIscontinuity Tracking for complex 2D shock interactions
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Added by
Mirco Ciallella
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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A new shock-tracking technique that avoids re-meshing the computational grid around the moving shock-front was recently proposed by the authors [1]. This paper describes further algorithmic improvements which make the extrapolated Discontinuity Tracking Technique (eDIT) capable of dealing with complex shock-topologies featuring shock-shock and shock-wall interactions. Various test-cases are included to describe the key features of the methodology and prove its order-of-convergence properties.
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Traditional probabilistic methods for the simulation of advection-diffusion equations (ADEs) often overlook the entropic contribution of the discretization, e.g., the number of particles, within associated numerical methods. Many times, the gain in accuracy of a highly discretized numerical model is outweighed by its associated computational costs or the noise within the data. We address the question of how many particles are needed in a simulation to best approximate and estimate parameters in one-dimensional advective-diffusive transport. To do so, we use the well-known Akaike Information Criterion (AIC) and a recently-developed correction called the Computational Information Criterion (COMIC) to guide the model selection process. Random-walk and mass-transfer particle tracking methods are employed to solve the model equations at various levels of discretization. Numerical results demonstrate that the COMIC provides an optimal number of particles that can describe a more efficient model in terms of parameter estimation and model prediction compared to the model selected by the AIC even when the data is sparse or noisy, the sampling volume is not uniform throughout the physical domain, or the error distribution of the data is non-IID Gaussian.
There is a need to accurately simulate materials with complex electromagnetic properties when modelling Ground Penetrating Radar (GPR), as many objects encountered with GPR contain water, e.g. soils, curing concrete, and water-filled pipes. One of widely-used open-source software that simulates electromagnetic wave propagation is gprMax. It uses Yees algorithm to solve Maxwells equations with the Finite-Difference Time-Domain (FDTD) method. A significant drawback of the FDTD method is the limited ability to model materials with dispersive properties, currently narrowed to specific set of relaxation mechanisms, namely multi-Debye, Drude and Lorentz media. Consequently, modelling any arbitrary complex material should be done by approximating it as a combination of these functions. This paper describes work carried out as part of the Google Summer of Code (GSoC) programme 2021 to develop a new module within gprMax that can be used to simulate complex dispersive materials using multi-Debye expansions in an automatic manner. The module is capable of modelling Havriliak-Negami, Cole-Cole, Cole-Davidson, Jonscher, Complex-Refractive Index Models, and indeed any arbitrary dispersive material with real and imaginary permittivity specified by the user.
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