Discontinuity Preserving Scheme

Non-linear schemes are widely used in high-speed flows to capture the discontinuities present in the solution. Limiters and weighted essentially non-oscillatory schemes (WENO) are the most common non-linear numerical schemes. Most of the high-resolution schemes use the piecewise parabolic reconstruction (PPR) technique for their robustness. However, it may be impossible to achieve non-oscillatory and dissipation-free solutions with the PPR technique without non-linear switches. Most of the shock-capturing schemes use excessive dissipation to suppress the oscillations present in the discontinuities. To eliminate these issues, an algorithm is proposed that uses the shock-capturing scheme (SCS) in the first step, and then the result is refined using a novel scheme called the Discontinuity Preserving Scheme (DPS). The present scheme is a hybrid shock capture-fitting scheme. The present scheme has outperformed other schemes considered in this work, in terms of shock resolution in linear and non-linear test cases. The most significant advantage of the present scheme is that it can resolve shocks with three grid points.

Comparison of a modified large-particle method with some high resolution schemes. Two-Dimensional test problems

Исследуются вычислительные свойства предложенной ранее новой модификации метода крупных частиц на основе нелинейной коррекции искусственной вязкости на первом (эйлеровом) этапе и гибридизации потоков на втором (лагранжевом и заключительном) этапе, дополненной двухшаговым алгоритмом РунгеКутты по времени. Метод обладает вторым порядком аппроксимации по пространству и времени на гладких решениях. На примере тестовых задач сверхзвукового потока газа в канале со ступенькой и двойного маховского отражения подтверждена работоспособность и вычислительная эффективность метода в сравнении с современными схемами высокой разрешающей способности. A number of computational properties of the previously proposed new modification of a largeparticle method are studied on the basis of a nonlinear correction of artificial viscosity at the first (Eulerian) stage and a hybridization of fluxes at the second (Lagrangian and final) stage supplemented by a twostep RungeKutta algorithm in time. The method has a second order of approximation in space and time on smooth solutions. The computational efficiency of the method is shown compared to several modern high resolution schemes using the forward facing step problem and the double Mach reflection problem.

Comparison of a modified large-particle method with some high resolution schemes. One-dimensional test problems

Проведен сравнительный анализ вычислительных свойств модифицированного метода крупных частиц на примере одномерных тестовых задач газовой динамики в широком диапазоне параметров течения. Численные результаты сопоставлены с автомодельными решениями и данными, полученными по схемам высокой разрешающей способности от второго до шестого порядков аппроксимации. Представленная схема продемонстрировала вычислительную эффективность и конкурентоспособность. The paper presents a comparative analysis of the computational properties of a modified large-particle method on one-dimensional gas dynamics test problems in a wide range of flow parameters. The numerical results are compared with self-similar solutions and data obtained by high-resolution schemes from the second to the sixth order of approximation. It is shown that the presented scheme is numerically efficient and competitive.