<html><body><div style="direction: ltr; font-family: Aptos, Arial, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">Dear FLASH users,</div><div style="direction: ltr; font-family: Aptos, Arial, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);"><br></div><div style="direction: ltr; font-family: Aptos, Arial, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">I am running laser-slab-like simulations, with a planar Al target and a He filled chamber. Depending on the equation of state I use, I see rapid oscillations develop in the temperature near the Al-He interface, where there is a jump in density, even if no laser is turned on. These oscillations can grow suitably large such that FLASH dies with either a c^2<0 error or negative 3T error. I believe that these errors are due to a breakdown in the numerical evolution, with the discontinuity not well handled, and not the EoS, which I’ve verified only has positive energy and positive c^2. Notably, I see the same errors develop with a simple solid-like equation of state,</div><div style="direction: ltr; font-family: Aptos, Arial, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);"><br></div><div style="direction: ltr; font-family: Aptos, Arial, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">P = K/rho_0 (rho/rho_o - 1) </div><div style="direction: ltr; font-family: Aptos, Arial, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);"><br></div><div style="direction: ltr; font-family: Aptos, Arial, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">with the internal energy determined by the thermodynamic relation rho^2 dE/drho = P. Note the above pressure is negative, but c^2 = dP/drho > 0.</div><div style="direction: ltr; font-family: Aptos, Arial, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);"><br></div><div style="direction: ltr; font-family: Aptos, Arial, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">I’d love to hear if anybody out there has had similar experiences and about any remedy. I’ve tried obvious remedies like increasing artificial viscosity to no avail. </div><div style="direction: ltr; font-family: Aptos, Arial, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);"><br></div><div style="direction: ltr; font-family: Aptos, Arial, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">Thanks for reading!</div><div style="direction: ltr; font-family: Aptos, Arial, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);"><br></div><div style="direction: ltr; font-family: Aptos, Arial, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">Best,</div><div style="direction: ltr; font-family: Aptos, Arial, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">Paul</div></body></html>