We present a novel adaptive-resolution particle method for continuous parabolic problems. In this method, particles self-organize in order to adapt to local resolution requirements. This is achieved by pseudo forces that are designed so as to guarantee that the solution is always well sampled and that no holes or clusters develop in the particle distribution. The particle sizes are locally adap...

In previous work, a new adaptive meshfree advection scheme for numerically solving linear transport equations has been proposed. The scheme, being a combination of an adaptive semi-Lagrangian method and local radial basis function interpolation, is essentially a method of backward characteristics. The adaptivity of the meshfree advection scheme relies on customized rules for the refinement and ...

In this paper we enhance the well-known fifth order WENO shock-capturing scheme by using deep learning techniques. This fine-tuning of an existing algorithm is implemented training a rather small neural network to modify smoothness indicators in improve numerical results especially at discontinuities. our approach no further post-processing needed ensure consistency method. Moreover, formal acc...

In this paper we study the efficiency of Strong Stability Preserving (SSP) Runge–Kutta methods that can be implemented with a low number registers using their Shu–Osher representation. SSP have been studied in literature and stepsize restrictions ensure numerical monotonicity found. However, for some problems, observed are larger than theoretical ones. Aiming at obtaining additional properties ...

Capacitance–resistance models (CRMs) are semi-analytical methods to estimate the production rate of either an individual producer or a group producers based on historical observed and injection rates using material balance signal correlations between injectors producers. Waterflood performance applied evaluate waterflooding effect forecast development index basis Buckley–Leverett displacement t...

This paper was selected for presentation by an SPE Program Committee following review of information contained in an abstract submitted by the author(s). Contents of the paper, as presented, have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material, as presented, does not necessarily reflect any position of the Society of Petroleum...

Physics-informed Neural Network (PINN) is a promising tool that has been applied in variety of physical phenomena described by partial differential equations (PDE). However, it observed PINNs are difficult to train certain “stiff” problems, which include various nonlinear hyperbolic PDEs display shocks their solutions. Recent studies added diffusion term the PDE, and an artificial viscosity (AV...

This paper presents the work of predicting oil production using machine learning methods. As a method, multiple linear regression algorithm with polynomial properties was implemented. Regression algorithms are suitable and workable methods for based on data-driven approach. The synthetic dataset obtained Buckley-Leverett mathematical model, which is used to calculate hydrodynamics determine sat...